you seem to very much focus on Muslims being the problem here, the economy will have a huge influence. As economies get bigger, women will have carreers and less time for more than two kids. Education is generally better when economies are better so people make better decisions in terms how many kids they can support.
On the other hand one could argue that better economies increase childbirth. I read different things now.
By disregarding all those variables you seem to be painting a very shortsighted version of the truth.
I agree though that cultural differences/ politics are a huge factor as well.
But the more people we have on earth the more potential there is one person finds a solution for making uninhabited areas on earth inhabitable.
Making desert land fruitful, creating water out of dry air. Moving to Mars and colonize there.
We humans are very resourceful
you still have not explained the population explosion in West Europe, one of the richest regions of the world with the best education systems. You don't explain why Russia with it's broken economy has a population that shrinks.
You want to go live like in an ants nest in siberia or the sahara? Go for it!
I want to enjoy space and freedom to roam in unspoiled nature.