A reader speculates
I think the way it works for everybody is roughly like this: Jesus said No one comes to the Father except through Me, but He never said it had to be on this side. I believe for everyone it happens on the other side, first thing, and without the operation of free will as we know it here. A man’s life gives the answer to this question, his religious brand loyalties aside (and irrelevant, although some religions are far better than others at getting people ready for that moment). Because of this I think pious Jews like the Orthodox guy who gave his life to save the helpless man on 9/11 will be overjoyed to see Jesus, and vice-versa. We’ll run and jump into the fires of Purgatory too, just to be with Him later. If we’re lucky.
I’m afraid you are wrong about the “second chance to repent after death part”. The Church teaches that probation ends at death. If you have definitively rejected Jesus in this life (and only he knows whether you have) there is no second chance after death. (Rejecting a label called “Jesus” does not necessarily mean you have rejected the person of Christ.) If you have not, however tentatively, “come to the Father” before death, you cannot do so afterward. It is true that Purgatory exists and that those whose sincere attempts to “coming to the Father” in this life have been marred by sin or ignorance will be fully cleansed in the next. It’s also true that this will all be through the grace of Christ, since he is God the Son. But it’s not true that those who lack justifying faith and simply refuse to come to the Father in this life will have the chance to do so in the next. That’s the catechism’s teaching, not just mine.