DUBAI—It isn’t just about Bibi.

The Israeli prime minister’s public confrontation with President Barack Obama over the U.S. administration’s pursuit of a nuclear bargain with Iran may have drawn all the spotlight this week. But America’s other key allies across the Middle East—such as Saudi Arabia, Egypt and the United Arab Emirates—are just as distraught, even if they lack the kind of lobbying platform thatBenjamin Netanyahu was offered in Congress.

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