It's not a secret the Israeli Defense Forces get a lot of help from their longtime ally, the United States. One IDF general even stated his belief the IDF gets more support from the American taxpayer than the Israeli taxpayer, though the math on that is fuzzy and he was probably just exaggerating for emphasis. The U.S. spent $3.15 billion every year from 2013-2015 and is slated to continue that support through 2018.
So when Israel sends a list of military hardware to purchase from the United States, one would assume it always includes the latest and greatest in military technology. After all, Israel's Iron Dome missile defense system, capable of detecting and intercepting incoming rocket attacks from Lebanon and the Gaza Strip, can intercept most missiles fired at population centers and even operate automatically.
So why would the Israelis request an airframe without stealth capability? Though they did request some of the developing F-35s, they opted to buy a proposed, unmade version of the F-15. Aircraft with stealth capability are designed that way at conception, since much to do with the stealth capability is about the shape of the aircraft (see: B-2 Bomber), which means, the Israelis are buying an undeveloped, much less stealthy plane, one which is inferior to the F-35, for a discount of only $10 million less.
Defeating stealth technology is a goal for defense manufacturers and U.S. rivals worldwide and has been for decades. The Israelis' primary threats operate at many different levels of technology and capability. Even without stealth technology, the IDF has proven itself time and again, throughout Israel's history to be efficient, lethal, and accurate while taking minimal losses in manpower and equipment.
There could be a number of reasons why the Israelis opted for a less invisible fighter, but the top of the list could be that they just don't care, they're just that good. In the Six-Day war, the IDF almost entirely destroyed the Egyptian Air Force while crippling Jordan, Syria, and Iraq's. In 1973's Yom Kippur War, the Israeli Air Force was outnumbered 3-to-1 and took heavy losses from Egyptian surface-to-air (SAM) missiles, but still bested the Syrians and Egyptians in less than a month.
Israel's current fleet of fighters and attack aircraft is made up of F-15 Strike Eagles and F-16 Fighting Falcons. The F-16 already beat an F-35 in a dogfight ... maybe the Israelis are onto something.