How do they stop a non-Muslim from visiting?
There are roadblocks stationed around the city, for starters. Some people have sneaked in, the most famous of which was British explorer Sir Richard Francis Burton.
Liberals who screech about the Boy Scouts keeping atheists out have nothing to say about Muslim religious discrimination, or much of anything negative to say about the Muslims, since they have the leftist virtue of being virulently anti-Western. Christianity and Judaism, being pro-Western, are of course fair game on all fronts.