Israel doesn't stamp passports, but adjacent countries do. That means you get a stamp entering or leaving Jordan or Egypt, perhaps someday Lebanon or Syria. That Jordanian or Egyptian stamp lists a specific border station at which the only possibility is that you entered or departed Israel. Anyone studying your passport will know what happened. They don't need to see an Israeli stamp.
I've never been completely clear as to whether having entered Israel will actually keep you out of, say, Sudan, which is the country southbound travelers worry about most. There are certainly problematic sequences of countries elsewhere in the world; for example, I've got a loose visa plus entry and exit stamps for Artsakh (a.k.a. Nagorno Karabakh), which if they were entered permanently in my passport would keep me out of Azerbaijan. But with the only evidence I entered Artsakh kept separate from my passport, it looks like I merely stayed in Armenia.
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