I've read from a couple of sources that in the 12th century, Constantinople had a significant Muslim population that managed to live pretty normal lives. These sources didn't seem the most trustworthy though, so I'm wondering whether this is accurate. Would the 1st Crusade not have been a cause of tension? There was also something about a popular mosque that was destroyed by the 4th Crusade, but I can't tell whether this is a rumor or if there's significant documentation to back it up. Details like that would be appreciated. Thanks for your help!
I answered a similar question in the past:
Hopefully that helps answer your question as well. In brief, there were certainly mosques and synagogues in Constantinople, and there were also numerous churches for the various different kinds of Christians. It wasn't a religious utopia though - the mosques and synagogues weren't allowed to be within the walls of the city (they were in the suburbs), and there were tensions with the Latins during the crusades, leading to a massacre of Latin merchants in 1182.