I was born and lived in Dubai for 20 years. From what I can tell they usually do not censor unless its sexual and accessed by their own country residents. Even then their censorship extends only through their goverment run service provider i.e. Etisalat. So a private provider can give access to the internet however they see fit but it costs a bit more. They are promoting their city as a business hub and a metropolitan destination. Causing to many uncomfortable restrictions is considered bad for business. They are pro American and British.
They should not care under normal circumstances unless there is something insulting their Country, Flag, religion and creates a controversial hue and cry. Its one of the only Arab countries where foreigners can wear a bathing suit and the women are not required to cover up. However they cannot sunbathe nude.
When I was there trying to access a remotely sexual site like Boris Vallejo on the internet was freaking tough as they blocked access to all known sites. My dad told me about the private server providers and how they differed.