In Britain, ten percent of the people under 25 are Muslim. The remainder are not all ethnic British either, but suppose they were. The ten percent Muslim women have four babies each, the ninety percent British have 1.5 babies each. The next generation is nearly a quarter Muslim, and the generation of Brits after that is outnumbered in their own land.
Actually, Muslim birth rates in most countries have fallen off a cliff in the last decade or two, dropping much more rapidly than they did in Western countries.. Iran now has a lower fertility rate than France or UK (or us).
Muslim immigrants to western countries generally have a somewhat higher birth rate than natives, partially due to the age at which people usually immigrate. However, this rate is dropping rapidly and is likely to converge with the native birth rate in about a decade.
Which means we won’t see the demographic exponential growth rate of the Muslim population you describe.
Which is not to say that Muslim immigration isn’t problematic for a bunch of reasons, merely that they aren’t likely to become a majority by having more babies. 10% or 20% Muslim population is itself a real problem if they adhere to Islamism.
Also, Muslim (and native) birth rates are of course subject to change, so anything could happen.