Introduction
I've been conversing with a lot of non-Catholic Christians lately and I feel convicted to share the answer to a question that often comes up in discussions with them. "Are you saved?" or "Can you be assured of your salvation?" To which I can answer, "yes," to the best of my understanding of how salvation works as taught by the Church. I'll do my best to explain the common view from non-Catholic Christians as well as the Catholic position. (Scroll down to the very last section if you only want the summary without the full explanation. If you are wanting to engage in a fruitful discussion however, I would advise reading the whole thing).
The Common Non-Catholic Christian View - Faith Alone
Most Non-Catholic Christians and Protestants believe in a Sola Fide model, otherwise known as "by faith alone." This comes from a selective reading of certain passages in Scripture that say if you believe and have faith in Jesus, you will be saved.
Romans 10:9 - "For if you confess with your mouth that Jesus is Lord, and believe in your heart that God has raised him up from the dead, you shall be saved."
John 3:16 - "For God so loved the world, He gave his only begotten Son; that whosoever believes in him, may not perish, but may have life everlasting."
Romans 3:28 - "For we account a man to be justified by faith..."
Romans 5:1 - "Being justified therefore by faith, let us have peace with God, through our Lord Jesus Christ..."
Galatians 2:16 - "...we may be justified by the faith of Christ, and not by works of the law: because by the works of the law no flesh shall be justified."
I could go on with more and more verses, but you get the idea. And thus, the argument that by faith alone persists. But what of other requirements such as Baptism which many Christians believe confers the forgiveness of sin?
Since these non-Catholic Christians believe that you are saved through faith alone that Baptism is an outward symbol of that faith which they at least admit, Jesus commanded us to do. They feel the same about the Eucharist as well; just a symbol that Jesus commanded us to practice after belief. But what does the Bible show us?
The Catholic View of Baptism
I'm going to take us on a journey that will answer the previous questions along the way. How does one receive the salvation that Jesus promises in the Catholic view?
First, Catholics believe that Baptism is the first means of salvific grace that we receiving which is a freely given gift from Jesus (and not a work) which washes away all sins. Where does this come from in the Bible? Several places actually:
Mark 16:16 - "He that believes and is baptized, shall be saved; but he that believes not shall be condemned."
1 Peter 3:21 - "This prefigured baptism, which saves you now. It is not a removal of dirt from the body but an appeal to God for a clear conscience, through the resurrection of Jesus Christ..."
Acts 22:16 - "Now, why delay? Get up and have yourself baptized and your sins washed away, calling upon his name."
Acts 2:38 - "But Peter said to them: Do penance, and be baptized every one of you in the name of Jesus Christ, for the remission of your sins: and you shall receive the gift of the Holy Spirit."
Romans 6 - "...are you unaware that we who were baptized into Christ Jesus were baptized into his death? We were indeed buried with him through baptism into death, so that, just as Christ was raised from the dead by the glory of the Father, we too might live in newness of life."
Taking all of this into context, the Bible says you must believe AND be baptized, "baptism saves you," do not delay and get baptized to wash away your sins, do penance and be baptized for the remission of sins and the gift of the holy spirit, and finally: you are united with Jesus in His crucifixion through Baptism.
These all look like very strong affirmations of receiving salvation, and the Catholic Church agrees.
But Isn't Water Baptism Symbolic?
Many non-Catholic Christians still insist that the water part of baptism is symbolic saying that all humans are born of water, referring to the actual birth process where a woman's water breaks and a baby is born through natural means. I don't know where C-sections come into this equation so I won't address that (that's on them anyways). The thing is, Jesus address this very thing to Nicodemus in John 3:4-6:
"Nicodemus said to him, "How can a person once grown old be born again? Surely he cannot reenter his mother's womb and be born again, can he? Jesus answered, "Amen, amen, I say to you, no one can enter the kingdom of God without being born of water and Spirit. What is born of flesh is flesh and what is born of spirit is spirit."
You can argue that Jesus is implying that being born of flesh is the same as being born of water, but He never says such a thing. In fact, refer to all of the above passages that demand baptism via water (and spirit) and tell me that Jesus meant that being born of water meant natural child birth.
Baptizing Infants and Children
Since the Catholic Church believes that Baptism and thus salvation is a gift from Jesus and not a work, it can be freely given to anyone. There are caveats of course. You can't give a gift to someone unwilling to receive it, so for those of an age of reason, they must do so of their own free will. For children, however, so long as an adult who is responsible for their faith formation (parent, guardian, god-parents) promises to raise them in the faith, they can be baptized.
Where is this in the Bible? There are several passages that imply entire households were baptized, but you're right, it never explicitly says that children were baptized. But absence of something doesn't mean that it isn't true. The word Trinity isn't in the Bible, yet we believe in the concept of the Trinity because of what the Bible heavily implies. Jesus also says in Matthew 19:14, "...'Let the children come to me, and do not prevent them; for the kingdom of heaven belongs to such as these."
If baptism is the initial ordinary means of salvation, then it is imperative that we baptize the children of believers as soon as possible.
Where does Faith Come In?
The formula that non-Catholic Christians use is one that Catholic do technically believe in. You are saved by faith in Jesus through His grace. For adults, this is simple: If you desire to be saved by Jesus, whether because you fear hell, desire heaven, or out of love of God, then you have a faith that will lead you to salvation. If you have such a faith while seeking the ordinary means of salvation (baptism) then God will have mercy on you and consider you saved for all intents and purposes.
This is an exception to the rule that we learn about in the narrative of the thief on the cross next to Jesus who showed a desire for salvation, which we Catholics call a "baptism of desire." Similarly, those who die a martyr, even if they haven't been baptized are baptized through their faith and blood, a "baptism of blood" as Catholic call it. And the terms are all together, the ordinary means of baptism is known as "baptism of water." All three imply "and spirit," but the examples are all clearly laid out in Scripture.
Finally, if you have faith in Jesus, would you not desire to do all that He commands of you? To have faith in someone is to believe in their words and actions. To Catholics, it's clear that we must be baptized because Christ commands it of us, just as He commands us to love God and neighbor and to eat of the flesh of man.
What About Works?
A common objection to the Catholic view of salvation is that we claim that works have a part in the role of salvation. Above I mentioned that we believe in the formula of "faith in Jesus through His grace," but that is somewhat incomplete. We believe more fully that justification happens through "faith in Jesus, through His grace, working in grace." But what does that mean? To start, you have to look at grace in two different ways.
The first grace in that sentence is the justifying grace that we're all concerned about. It's the grace that comes from the love of God and His Son that purifies us and allows us to reach out to Him, purifies us through no merit of our own, and be with Him in heaven for all eternity. The second grace in that sentence refers to "actual grace," which I think is a confusing name for it. Think of it like this: If you have justifying grace, you will be with God in heaven. If you are given actual grace, it will help keep you in that state of justifying grace and empower you to do good works for the sake of His kingdom including working in His plan of salvation for others.
So what purpose are works as far as salvation is concerned? Basically, works keep you in the state of "being saved" and allow you to do things for the sake of God and His kingdom. It enables to you do things you otherwise wouldn't be able to do like "sin no more," which without God's gift (grace) would be impossible for man to do alone.
We do not believe that works alone can save you, much like Scriptures say about works of the Law. It's only through faith in Jesus through His grace that any of this is possible after all. And besides, if you have faith and are not performing works, your faith is dead as is made clear in James 2:14-26 (of which I will take selections; look the whole thing up for full context).
James 2:14 - "What good is it, my brothers, if someone says he has faith but does not have works? Can that faith save him?"
James 2:17 - "So also faith of itself, if it does not have works, is dead."
James 2:19 - "You believe that God is one. You do well. Even the demons believe that and tremble."
James 2:21-22 - "Was not Abraham our father justified by works when he offered his son Isaac upon the altar? You see that faith was active along with his works, and faith was completed by the works."
Galatians 5:6 - "For in Christ Jesus, neither circumcision nor uncircumcision counts for anything, but only faith working through love."
Can You Lose Salvation?
This one is difficult for non-Catholic Christians since many believe in a "Once Save; Always Saved" model due to many verses outlined in the "Faith Alone" section, as well as other quotes. But the problem is, there are various sections in the New Testament that show apostles being wary to not lose their faith and talk about sins which separate one from God.
Galatians 5:4 - "You are separated from Christ, you who are trying to be justified by law; you have fallen from grace."
Philippians 2:12 - "So then, my beloved, obedient as you have always been, not only when I am present but all the more now when I am absent, work out your salvation with fear and trembling...
1 John 5:16-17 - "If anyone sees his brother sinning, if the sin is not deadly, he should pray to God and he will give him life. This is only for those whose sin is not deadly. There is such a thing as deadly sin, about which I do not say that you should pray. All wrongdoing is sin, but there is sin that is not deadly."
Thus, we see that we can 1) fall from grace 2) we must continue to work out our salvation and 3) there are different types of sin, one of which is deadly which Catholic believe is the type of sin that cuts one off from God.
So if you can lose salvation, how can you gain it back? Through the sacrament of confession.
Means of Re-attaining Salvation Once Lost
There are various ways for you to attain the forgiveness of non-deadly sins. Asking the person you offended in sin for forgiveness, sacrificial works, the Eucharist, and simply prayer to God the Father or Jesus asking for their mercy and forgiveness. These are all sufficient means of receiving forgiveness of non-deadly sins, but what about sin that separates us from God?
For this Jesus instituted the Sacrament of Confession. I won't get too deeply into it, but I'll drop some Bible quotes that point to priestly confession as Catholics understand it.
John 20:21-23 - "Jesus said to them again, "Peace be with you. As the Father has sent me, so I send you." And when he had said this, he breathed on them and said to them, "Receive the holy Spirit. Whose sins you forgive are forgiven them, and whose sins you retain are retained."
James 5:14-16 - "Is anyone among you sick? He should summon the presbyters of the church, and they should pray over him and anoint [him] with oil in the name of the Lord, and the prayer of faith will save the sick person, and the Lord will raise him up. If he has committed any sins, he will be forgiven. Therefore, confess your sins to one another and pray for one another, that you may be healed. The fervent prayer of a righteous person is very powerful."
Mark 2:10 - "But that you may know that the Son of Man has authority to forgive sins on earth--"
Leviticus 5:5-6 "...when someone is guilty in regard to any of these matters, that person shall confess the wrong committed, and make reparation to the LORD for the wrong committed: ...Thus the priest shall make atonement on the individual's behalf for the wrong."
From these we see in order: Jesus grants the apostles the ability to forgive sins, that presbyters (priests) should pray over and anoint the sick and in doing so his sins will be forgiven, that Jesus as the Son of Man (in the flesh) has the authority to forgive sins (and thus anyone He grants this power to), and that in the Old Law priests were given the charge of being confessed to and offer those sins to God which is a prefigurement of the New Testament way of confessing through priests to Jesus.
But isn't Jesus our only mediator to God the Father? Of course, but there are many ways to Jesus including through a priest, your fellow man who spread the Good News to you, the Bible which holds the Good News, etc...
Other Things Necessary for Salvation
So we have baptism (through water, desire, or blood + spirit) and confession to regain salvation if lost. Are there any other conditions of salvation under the Catholic view? Yes, there is one more and that is the Eucharist. Since that is a large topic on its own, I will point you to my other article that focuses on the Eucharist here: https://www.yomic.org/2011/02/transubstantiation-body-and-blood-of.html
What about Those Outside of the Faith and Other Exceptions?
Since God has infinite mercy and love for mankind despite its wickedness, there may be the possibility of salvation for those who don't meet all of the conditions I have listed here, but it is only through Jesus that this is possible. For this, I'll refer to some quotes within the Catechism to give a more full explanation for this case so I do not accidentally say something incorrect:
This affirmation is not aimed at those who, through no fault of their own, do not know Christ and his Church: “Those who, through no fault of their own, do not know the Gospel of Christ or his Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do his will as they know it through the dictates of their conscience – those too may achieve eternal salvation” (quoting, Lumen Gentium, 16).
“Although in ways known to himself God can lead those, who, through no fault of their own, are ignorant of the Gospel, to that faith without which it is impossible to please him, the Church still has the obligation and also the sacred right to evangelize all men” (quoting Ad Gentes, 7, another document from Vatican II).
Summary and Conclusion
So in order to be saved in the Catholic Church's view, a person must be baptized, receive the Eucharist, and maintain a "state of grace" throughout his or her life. If that state of grace is ever lost, they must go to confession or if they perish before going to confession, but fully intended on going at the next earliest possibility, they will be forgiven as well.
Those Christians outside of the Catholic Church, if they are totally convinced that they are following Jesus' teachings to the best of their ability, but happen to be wrong about certain things, they may be shown mercy.
Those outside of the Christian faith entirely, if they are following what God has written on their hearts (Romans 2:15) and are truly seeking God with a sincere heart, they may also be shown mercy.
God desires all of mankind to be saved, justified through Jesus and working for the good of the kingdom of God, therefore He calls us all to Him. Unfortunately, the world can twist and distort the truth for some of us, so as along as we are seeking Him and following Him to the best of our ability, I believe that God will have mercy on us for none are worthy in the first place, but through His Son we can be redeemed.