It is also punishable by death in the majority Christian country of Nigeria. It is also illegal in other predominantly Christian countries, like Uganda. Additionally there are also predominantly Muslim countries that do not criminalize homosexuality. Let's also not forget that in many European places it is only a couple decades since homosexuality was decriminalized.
Of course the Muslim countries in the middle east, and some in Africa, are extremely oppressive regimes ( though, a lot of the refugees are actually fleeing from extremely radical Islam), but the image that these people are savages, that can't understand our civilized ways is just severely flawed.
Islam can be just as moderate as Christianity, even though either source material isn't.