There are two important distinctions here - whether a person really is rejecting God (as in, has he/she really heard the Gospel, or a caricature of it, or not at all), and why that person is rejecting God.
I mention the latter because things like abuse (be it emotional, physical or sexual), lack of compassion, condemnation (especially when the person is not even sinning) etc. from outwardly devout family, parish members, or even worse, a priest, can rob someone of their faith. Those people make the Gospel into a caricature, and the resulting apostasy often happens unwillingly. In those cases, I think the people guilty of that robbery should worry more about their own salvation, than that of the apostate, who may still have his or her faith buried somewhere.
As for remote cultures where other religions (or in some cases lack of such) are dominant, I think most people aren’t guilty of rejecting the Gospel. Take Japan as an example - even if the Church has existed there for centuries (albeit underground for some of those centuries), the average Japanese person is close to clueless about what Catholicism is. It seems to be very popular in media etc. because of its foreignness, but people are still completely (and in some cases hilariously) clueless about the content of our Faith. But in any case, if that person seeks good, and maybe even some concept of God, I can’t see any reason why that person should not be saved. In many ways, I fear they are less guilty of rejecting God than many Protestants (who reject the Church, even despite knowing better, in some cases), and even some Catholics (who really should know better ).
As for Augustine’s view on the salvation of remote peoples who have not heard the Gospel (in case someone brings it up, hehe), I think that view is proved incorrect simply by actually interacting with them. His main intention was to counter Pelagianism, and rightly so, but he seems to have thrown the baby out with the bath water, so to say. At the same time, not even Feeney was condemned as a heretic (the excommunication was for other reasons, and was lifted without any renouncement of his theology, if I remember correctly), so there’s a large spectrum of apparently valid (if non-heresy equals validity) conclusions here. I won’t hesitate to say Feeneyism, and even Augustine’s view, is wrong, though.