Is the religion the cause or merely a tool being used?
Islamic State are called 'Islamic State' for a reason. Commit 10000 atrocities with that name and people will eventually think it's 'Islam'. Tell the same lie 10000 times and people will think it's true.
They don't even have to rely on immigration, with social media they can brainwash/recruit anyone with the right psychological structure/life experience anywhere. Break them down, play their anger/psychopothy like a violin, mentally separate them from the world around them and after some careful brainwashing/grooming you've got a teenager/relatively young person lacking critical thinking skills driving a truck at a large crowd of innocent people.