No, it does not. In addition, to open a visa to the UAE, it is enough to provide just a copy of the first page of the passport, not the passport itself. Many years ago, there the immigration authorities had an implicit rule to restrict the entry to the UAE of people who had previously visited Israel. But then, just behind the scenes, this rule was canceled.

Not affected at the moment. But if you are worried, then ask the Israeli border guards to put a stamp not in the passport, but in a special ticket.