You have put your finger on the real problem. The West has become hostile to procreation. That is why it is being overrun.
I think it's more than that - the West has become hostile to life in general, life as it really is. I hate to say "we," because it annoys me when people "we" and I don't think it includes me :-), so "a significant element in our society" seems only to want the kind of life that can't be achieved without dreadful inhumanity: a life in which sex doesn't make babies; people don't become old, sick or incapacitated; a spouse is never unsatisfactory; "somebody" provides exactly what we want without an inconvenient level of effort.
If one can get life to work that way, one doesn't need God, but can imagine oneself as God.