I think the problem here is dating for us Christians is with a view to marriage, not immediately after the first date or anything obviously
, but still that is the end game as they say. So from the start you are at least looking for some things that indicate the person will be a potential future spouse, compatibility, character, some form of chemistry possibly, anyway yo see where I'm going, and yes being a Christian is an important mark in a future spouse. Both the advise from the OT for Israel and how it is carried forward and expressed anew by Paul for the community of the church that is the people of God by faith into the Messiah, is that we should not be yoked with unbelievers (assuming we are not already married, which is different situation).
This is not some arbitrary or killjoy advice, but rather deeply pastoral and wise, because beyond the fact you might never see the one you love making a declaration to follow Jesus and accept His Lordship and saving and victorious death and resurrection, and depending on your eschatology view on what happens in the resurrection and final judgement (eternal conscious torment, conditional immortality/annihilationism or evangelical universalism) this might not be as painful, but all might have you concerned about at least some of their future there, depending on other factors on their character and it's growth particularly in more destructive ways. That itself is a terrible burden to bear, with the thought that their salvation is your responsibility alone, when it is God's, but it can be very difficult to leave it alone when you love them so much.
2ndly, the problem of very different world-views comes into play, I tend not to prefer the term atheist myself, it isn't very informative (under certain perspectives, such as ancient Rome, Christians would be classed as atheists and were so called
), rather in the West most operate under the post-Enlightenment Epicureanism that came to full flower through the Enlightenment (most commonly know as secularism/modernism today) usually operating with post-modernism critique and sentiments incorporated into that belief system. Sadly often enough Christianity itself has adopted the same framework with some tweaks (talk of supernatural and natural comes into play here), but that is beside the point, rather it is a very different world-view/narrative to the Judeo-Christian one, and so what is seen as of prime importance, the values, aims and purposes someone (whether atheist, agnostic or somewhat of Deist) who holds to secularism is in stark contrast in some key areas of the Christian spouse. This will inevitable lead to family conflict, particular over some decisions on the future, children and their future and all sorts of aspects of your lives together, and either you will be in continual battle or one will have to bow before the will of the other. Neither situation is a healthy marriage or family life (and particularly not a Christ-lead one) so I know it can be hard, by yes, the Bible doesn't warn against marrying unbelievers because it's trying to spoil a future for you, rather the opposite, it's giving the advise to help secure one
.
Anyway, those are my thoughts, I hope they help, and God bless and grant wisdom to those in such difficult situations or facing such hard choices.