It’s not only the Iron Dome. The UAE and some other Gulf countries have expressed interest in various Israeli missile defense systems. We are talking about Billions of USD in potential sales that Israel is refusing to sell. Apparently the UAE has gone from expressing interest to pressuring its new friend and ally Israel to make it happen.
So why hasn’t Israel obliged?
The UAE has full trade and other ties with Iran even to the point of helping Iran bypass the international embargo against it. Indeed the Emirates seems to be pivoting towards Iran recently, perhaps as a hedge against the perception that the USA is leaving the region militarily. Israel feels it can not afford to have such sensitive defense technology in the Gulf, where Iran can either get hold of it or access it in order to understand it better for improving Iranian missile technology.
As an aside, it will indeed be a quirk of fate if say Saudi Arabia which does not yet have official ties with Israel, but has nevertheless expressed interest in various Israeli anti-missile defence systems including the Iron Dome, ends up receiving such systems before the openly much friendlier UAE does.