Be careful about joining the ancient prayers, though, unless you know how to perform them, and have converted to Islam. Otherwise you'll really offend people.
Anyway, if you go up to any mosque and find a person you can ask, hey is it okay if I check this place out? Can I join in the prayer? Unless you meet an old uncle from the old country, they'll probably welcome it.
The mosque I go to now, in Edmonton, we have this guy that comes for the potluck. One day, the prayer is starting and I tell him, let's go pray (we were cleaning up) at which point he tells me he's not Muslim! Anyway, no biggie, he continued cleaning up while we prayed :)
Now that said, I'd buy you could easily offend someones religious sensabilities by praying an incorrect way, but you can also easily offend someone by not praying at all...
If something, like, oh, say islam's apostate laws, existed, it would be plain to everyone that you can't have freedom of religion and islam (not limited, of course, to that one religion). Only one of those can exist.
Of course that doesn't mean you can't just deny any of this exists, especially because there are liberal muslims (less than 1%, sure, but of course it doesn't look like that in San Francisco. But even in San Fran you won't have any trouble finding people who'll use violence against apostates either).
No ?
Then, sorry to say, it's not comparable to what happens in the middle east at all.
And God forbid it's a woman were to try that.
There are some types of non-muslims (open apostates) that would be putting themselves in real physical danger by entering your average mosque in Islamabad and praying. We have a local ex-muslims meetup in London and stories of threats + actual physical violence from family and "community" are more common than not.
It also goes without saying that if there's no women's section and you have a vagina, you're shit out of luck.
Disagree with this, they'll likely be overjoyed that someone foreign shows positive interest in their religion.
There are some things you have to do before going to a mosque: unlike churches, you can't get in a mosque "just to visit" (except if they have open-hours for non-worshippers/tourists, which is unlikely for a mosque in the middle of Yemen). You have to be in a state of purity (http://www.onislam.net/english/reading-islam/understanding-i... Also, joining the prayer if you're not muslim can be troublesome, but by all means if you just get in the mosque and maybe observe people praying, I'm not sure you'll get in any trouble. Theoretically, even a rude behavior in a mosque shouldn't cause you any big problem (a man once urinated inside the prophet's mosque, and the prophet stopped some believers that wanted to punish him and just covered the part where that man urinated).
Muslims are really friendly with non-muslims that are geniunly interested (even in mosques where there are some rules to respect)
In my experience, the biggest challenge you face in visiting a mosque is that people will make a sincere effort to convert you to Islam. They do this out of generosity and kindness, but it leads to some intense conversations. It is best to be ready with some good deflecting answers, unless you are considering becoming a Muslim.
I was very surprised to find myself invited to enter nearly every mosque I visited in Yemen. The only exception was the Great Mosque in Sana'a, which is closed to nonbelievers. My guess is this is because Sana'a sees a relatively large number of tourists compared to the rest of Yemen.
It would be hard to overemphasize the positive, welcoming, generous attitude of Muslims towards anyone with a sincere interest in their religion.