It always felt to me that the people sounding the horn on population collapse just think that not enough of the "desirable" people are being born.
Culture evolve with how we live anyway, and you cannot really 'preserve' a culture that didn't exist 70 years before and will be different in 50 years anyways. What people really mean by 'preserving our culture' really is 'preserving our heritage'. That will be done as long as no 3rd world war happens.
If you won’t, someone else will and you’ll be a part of theirs from that point on (or dead).