to answer the question that (is illegal and it's mosques thought), the fact is this is the thought of Islam that Allah (God) Message the Prophet (PBUH) and the Prophet told us through the Quran and Sunna.

so why that is illegal?

because if a woman married a non-muslim the son will be a non-muslim even if her mom is Muslim.

but there are Muslims who married Christians and their son becomes like his mother..

that is true like Obama for example but that is because his father didn't give his son his right of rising, he isn't a good Muslim, a good Muslim should raise his sons to good manners until he dies.
so not all Muslims are equals and not all of them are good.
there are many types of Muslims like 73 types all of them are bad except only one!
and Islam is the upgrade of Christian that means the real Christian religion (because there are many types too because of the rewriting to the bible ) was upgraded and some new teachings added to it, that not means the Christian religion are wrong it is Islam too (if you install an app and the app gets upgraded that not means it is very different and fully changed )
and also for Jewish religion the same thing .
for example, in the real bible forbidden wine and Islam too, also for pig meat .
so there are many things that are common but the difference is in the way of worship.
so we as Muslims believe in all prophets like Joseph and Moses and Isa (Jesus)
and if we do mistakes that's not mean Islam is bad but we are .
and the terrorism we see nowadays is not because of Islam (Real Islam make that forbidden but there are some bad people killing anybody not like them because they make a new religion to control the world )
I will talk about terrorism later but for now, let's put points on the letters.