Just to make clear, all unbaptized, non-Christians go to hell where they burn for all eternity. (And that includes aborted fetuses BTW, in case you don't know.) All Christians go to heaven, no matter how they've sinned. Jesus paid for their sins, and if they don't sin he died for nothing. (Except Unitarians, that last one. Unless they were baptized into another Christian church and then converted.)
So what about all the babies who've been Christened? Is that what you mean by baptism? If so then I guess most of the people from my generation will go to Heaven, as it was a pretty much automatic thing for our parents to Christen us ASAP. I never had my kids Christened, as I thought it would be better for them to decide if and when they wanted to be involved in any religion. So from what you say, they will all automatically go to Hell, no matter how good they are as human beings.
What you make clear is that lots of so-called Christians have messed up ideas, and are more preoccupied with their own future "salvation" in an afterlife than following Jesus in this one. Saint Paul (unfortunately the first to write about Christianity) started us down this road, and Saint Augustine took us over the cliff, with his doctrine of Original Sin. The Catholic Magesterium cushioned the blow with Limbo, a corner of hell where the poor babies don't burn but enjoy natural happiness. Unfortunately, they haven't committed (or non-committed) themselves as to whether or not the place exists. As for non-Catholics (Christian or non-Christian), there is no salvation outside the Catholic Church. But that doesn't mean that non-Catholics can't be saved. (leave it to the Jesuits to come up with this one). They are saved by their "invincible ignorance". That goes for Muslims and according to Pope Francis (speaking off the cuff) even atheists. When they get thru with the intricate rationcinations, I have the impression that the only person going to hell is me, who understands them and rejects them. But I have been baptized, twice--once as a Catholic infant and once as a Methodist adult. For non-Catholics, it depends on whether you're a literalist or not. Jimbee is serving us the Paulist doctrine that Jesus was the sacrificial lamb who died to atone vicariously for our sins.Evangelical and fundamentalist Protestants believe that, mainline Protestants not necessarily, Progressives like me tend toward Luke's alternative: Jesus' suffering made us aware of our own sins, for which we repent. In defensse of Paul, when h talks about salvation by faith rather than works, he doesn't seem to mean mere verbal or mental assent to a doctrine, but rather pistis (toπίστις)--faithful commitment to a new life in Christ. Not all Christians accept the idea that just calling yourself a Christian gets us to heaven, "no matter how they've sinned". Catholics don't believe that. Die with an unconfessed mortal sin on your soul and you go directly to Hell without passing Go. I think Hell is a metaphor for a world in which most people have given themselves over to idolatry--whoring after the false gods of wealth, status, power, and sensual indulgence--and turned their backs on the poor, the marginalized, and the stranger. Its Jaws are open wide to receive us--baptized or not !