Also, yes I agree there birthrate is higher in some parts of the world, particularly sub-Saharan Africa which has a large Muslim population. The number is dropping rapidly though.
If you are truly interested in the rates, look up Hans Rosling and his talks about the changes in childbirth rates, mortality, etc. He passed away several years ago but his research is still valid and is a great indication of which direction the planet is moving. Spoiler: life is improving on most metrics for everyone on the planet.
I agree, vast influxes of people can be detrimental for a time including putting a strain on housing. I also agree immigrants are being used to score polical points. Immigrants are not the cause of the house crisis, bad policy has brought us to this point.
The issues you have spoken about are not caused by immigration, sure immigration can put pressure issue or even make it worse but we should look at fixing the underlying issue rather than blaming people who weren't even in the country when the problem was created.
We can fix the system.