Paul Ryan objected to proposals for a ban on Muslim migrants, significant numbers of whom support some form of terrorism, entering America, insisting on a security test rather than a religious test for immigrants.
But when terrorism is a religion, then a security test becomes a religious test. There's just no way to get around that. Islamic terrorism is a religious phenomenon. Atheists don't commit Muslim terrorism. Muslims who believe in the fundamental principles of Islam do. And they do so in order to make Islam supreme over all religions. This is the core idea of the battle cry, Allahu Akbar.
If you want to screen out Muslim terrorists, then you are screening for a particular religious belief. Either that or you're doing nothing productive at all.