In the UAE, if you have an Israeli passport, you won't be allowed in, as they don't officially recognise Israel as existing. I suspect a lot of that is to do with them needing to be seen to show solidarity with some of their neighbours because as others have said, they do plenty of business with Israel & Israeli companies, however in many instances they use a non-Israeli 'front man' so the links are not so blatant - effectively UAE on the whole don't care but have to keep up a certain image to their neighbours
If you have an Israeli visitors stamp in your passport, there is a chance you won't be let in, however evidence as to what percentage of those with an Israeli stamp aren't let in is rather thin on the ground - I've heard everything from once in a blue moon (no pun intended!) to a significant chance of being refused entry
Theoretically however, you could visit UAE wearing full orthodox outfit, be called Shlomi Cohen, have a British passport and be let in. I wouldn't advise it though ! I have a number of Jewish friends who live/have lived in the UAE and they don't like to flaunt the fact they are Jewish to the point they are wary about bringing it up, but they don't live in worry either - they just think it's sensible to be low key about it there
Within the UAE, you see policies that are anti-Jewish rather than anti-Israel (such as boycotting of books by Jewish academics) but I honestly don't think our owners give a monkeys. There have been Israeli players, they will know we have a decent sized Jewish contingent of fans, half the club's life/honorary presidents are Jewish and they certainly wouldn't choose New York if they had an issue with Jews ! Put bluntly, I think they take a pragmatic & commercial view.