I’ve heard that you have to be a Muslim to be allowed into Mecca for the hajj. But do you also have to be a Muslim to live there? And are the holy sites in Mecca open for visits for people not taking part in a pilgrimage?
You must be a Muslim to enter or own property in the Two Holy Cities. The Harem (Forbidden) area is about fifty miles in diameter. Police checkpoints are on all the roads. The Meccah airport is just outside the area, so non-Muslims may use it.
The ring road is forbidden to non-Muslims.
Does that answer your question?
Thanks, Paul, that does answer my questions. If you have time for a couple more:
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What kind of proof is required to prove your are a Muslim?
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If I was a Muslim, and I wanted to visit one of the holy sites, but not make the entire pilgrimage, would that be allowed?
(Don’t worry, I’m not trying to sneak into Mecca ) 
I have a few questions about the religious police in Saudi Arabia. I’ve heard that when the times for prayer are announced, the religious police round up any men on the streets and force them into the nearest mosque for prayers. Is this true? Are women required to go mosques for prayer at these times as well? Also, do the religious police patrol in the mosques and make sure that everyone is praying? What happens if they see someone slacking? Finally, are there female religious police officers? Thanks for your observations.
At prayer time, all the stores close, so I tend to wander around.
I used to follow the religious policeman at one of our shopping mall on a fairly regular basis. Sort of like playing James Bond, hey I was bored.
A nice-looking little old man, no uniform, accompanied by a real policeman. He would go to all the coffee shops and touch all the Saudi-looking guys on the should and remind them it was time to go to mosque. They would say something and he would move on.
The Religious Police do do nasty things, they get in the paper from time to time, but my experience is not unusual. Since the RP do not have uniforms, anytime a busybody gets his panties in an uproar and chews someone out the RPs can get blamed.
As I said, this is not to say they do not do nasty things from time to time.
David-
Sorry in my pre-caffine condition, I ignored your questions.
The identity papers of us foreigners are marked with our religion. All Saudis are Muslims.
Muslims can visit the Holy Cities as they please. The can make the Umrah (‘Small Hajj’) with no special paperwork. (Pretty neat, if you live here it takes like twenty minutes. For most people it is an expensive adventure.)
Special paperwork is need for the Hajj, simply because of crowding.
Hajj visas are issued by Saudi Councils based on the number of Muslims in your country. They require a statement from your local Mosque as to your seriousness and good standing.
Does that answer your question?