A Muslim, a Jew, a Christian, and an atheist walk into a coffee shop...

[Catholic_Lady]

I'm glad I was able to explain it in a way that made sense. It took a while for me to understand it as well, and I still feel like a lot of your average, everyday Catholics don't quite understand if fully either. We often hear the simplified versions of this like "if you die in mortal sin you go to Hell" and "you must be a follower of Jesus to enter the Kingdom of Heaven"... and that's a real shame. It takes some digging deeper to put all the pieces together and understand that it is far from as simplistic as it seems. God is so much bigger than that, and humans are so much more complex than that. That's why the Church stresses that we must never judge the fate of a person's soul, with the exception of canonized saints who we fully believe are in Heaven. But as far as Hell goes, we have no idea who is there and neither can we assume to know. Even if they are Hitler, we can't make the claim that they are in Hell.

Even someone like Aquinas, whom, as far as I know, remains revered among Catholic intellectuals, argues (on the authority of Scripture and Church Fathers) that baptism is required to enter heaven, that all are condemned to Purgatory as a result of original sin, and that Hell is reserved exclusively for those who have failed to obtain forgiveness for mortal sins, which would include rejecting the Gospel stories as veritable fact.  In his account, ultimately works don't much matter apart from belief, as "without faith it is impossible to please God" (Heb. 11:6).  Are these not orthodox views within Catholicism anymore, or has the Church permitted its members more intellectual space to diverge from traditional interpretations?

Aquinas was a great theologian but his work is not church doctrine and therefore not dogmatic. Also, he was from a while back ago so it would make sense that he'd have a pretty old school view of the matter. As it stands now, the CCC talks about baptism of desire. This means even if a person was not physically baptized for whatever reason, he/she can be still be saved. Pay special attention to 1260:

 VI. THE NECESSITY OF BAPTISM

1257 The Lord himself affirms that Baptism is necessary for salvation.60 He also commands his disciples to proclaim the Gospel to all nations and to baptize them.61 Baptism is necessary for salvation for those to whom the Gospel has been proclaimed and who have had the possibility of asking for this sacrament.62 The Church does not know of any means other than Baptism that assures entry into eternal beatitude; this is why she takes care not to neglect the mission she has received from the Lord to see that all who can be baptized are "reborn of water and the Spirit." God has bound salvation to the sacrament of Baptism, however he himself is not bound by his sacraments.

1258 The Church has always held the firm conviction that those who suffer death for the sake of the faith without having received Baptism are baptized by their death for and with Christ. This Baptism of blood, like the desire for Baptism, brings about the fruits of Baptism without being a sacrament.

1259 For catechumens who die before their Baptism, their explicit desire to receive it, together with repentance for their sins, and charity, assures them the salvation that they were not able to receive through the sacrament.

1260 "Since Christ died for all, and since all men are in fact called to one and the same destiny, which is divine, we must hold that the Holy Spirit offers to all the possibility of being made partakers, in a way known to God, of the Paschal mystery."63 Every man who is ignorant of the Gospel of Christ and of his Church, but seeks the truth and does the will of God in accordance with his understanding of it, can be saved. It may be supposed that such persons would have desired Baptism explicitly if they had known its necessity.

1261 As regards children who have died without Baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus' tenderness toward children which caused him to say: "Let the children come to me, do not hinder them,"64 allow us to hope that there is a way of salvation for children who have died without Baptism. All the more urgent is the Church's call not to prevent little children coming to Christ through the gift of holy Baptism.

  
As you can see, the CCC leaves this issue fairly open, saying that "this is the way we know of, and so we take no chances", but then going on to say that God is not bound by the sacraments and that there are other ways to acquire salvation without the physical sacrament of baptism. 
I would argue that an atheist person or a Muslim person or whatever other non Christian person who genuinely just doesn't believe in Christianity and Christian baptism but seeks goodness, love, and virtue as best as he understands it, could fall under 1260.  
Now there are some Catholics out there who are super old school and who will think otherwise, but it is widely accepted among Catholics now a days that the physical act of baptism as a sacrament is not an end all be all to going to Heaven or Hell. And it wouldn't make sense that it would be.