It isn't a matter of competition.
It is a matter of giving up on the future or working toward the future.
If there are 1 billion Muslims going to 1.5B and there are 800M Westerners, going to 1B, say - the West isn't "winning" some battle of sheer numbers.
B ut it is maintaining and growing its population and remaining large enough to defend itself.
If there are 1B Muslims going to 1.5B and there 800M Westerners going to 400M, that's just cultural suicide.