Dubai is still plenty Muslim, dont worry about that. I was there during Ramadan in 2006, and even though Islam allows for non Muslims to drink and eat during daylight hours, it was a bad idea to do so. I was warned more than once about the Religious Police arresting Westerner's for drinking water in public during daylight. I was woke by mosques every morning I was there at 5am with the call to prayer. The hotel I stayed in had a tour group from Iran. I hung out with some of those guys for some of the time I was there, and you know what, they were awesome.
I had a great time staying where I was there, in the old part of Deria. Once the guest workers knew I was Australian, all they wanted to talk about was Cricket. I didnt feel threatened at all.