The basic datum is that the modern world is in essence divided into a minority of fertile traditionally/ patriarchally-religious people - who are having more than two kids on average; and a large majority of sterile atheist/ liberally-religious/ de-facto Leftist people (including those on the mainstream 'Right') who are going extinct.
The argument is over whether the minority-religious will eventually win and dominate, because of their fertility; or whether the mainstream-secular will win because they can deconvert the religious faster than the religious can breed.
One answer is that - unless they are exterminated - the religious will eventually win, because the sterile group cannot win (although they could perhaps be the last men standing). But the religious might win in a world with a much smaller population.
Another aspect is that most of the fertile religious (the exceptions are Mormons - a tiny minority in The West, and only significant in the USA) are either actively hostile to 'Western modernity' or at least non-participants and materially dependent on it.
On this scenario, the religious will win - but the world will revert to a pre-industrial, zero-growth agrarian society - the kind of society that could sustain 4 million people in England (c1600) compared with the current 65 million; or at a global scale a population of about 1 billion in c1800 compared with 7 billion today.
By such an account a large majority of the current population would certainly die - one way or another (from some combination of starvation, violence and/or disease); the exact number at any timepoint depending on how long a surplus people could live-off capital accumulation, compared with the effect of a currently lower level of human 'fitness' than 200 years ago, due to eight generations of dysgenic breeding and mutation accumulation.
Or we could take a wider and more religious-spiritual view; from which such matters are subject to divine influence and plans - the effect of which depends on perspective. I personally believe that (for various reasons, some material, others spiritual) we cannot 'revert' to a traditionalist economy or religion. That is: we cannot 're-set' to any earlier type of society.
So I would say - neither the sterile-Leftists nor the fertile-traditionally-religious will win; but what will emerge is something new and unforeseen.
In other words, the eventual 'survivors' will be different and will live differently from anything which has been seen before on earth.
I assume we are somewhere in the End Times; and further towards the end of the End Times, I think the earlier and present options will - for various reasons - close-off; and we will be left with a very clear and stark choice.
The 'we' to whom this refers may be an extremely small proportion of the population alive today - but not from any kind of divine 'punishment' for our (undoubted and extreme) sins, but simply because hardly anybody will have chosen to do what must be done. (There being no argument with 'must'.)
But of course the one incalculable is human choice. Men are truly agent, and will choose, whether or not they acknowledge that that is what they are doing.
The best scenario - and my best hope - is that when the choice comes we will all recognise it as a choice, and understand the implications.
After that, it is up to each, as an individual.