https://www.touristisrael.com/the-israeli-passport-stamp/974...
https://www.touristisrael.com/the-israeli-passport-stamp/974...
And to show how stupid things were--he also had a stamp he had made up to make forged entries on our yellow books. At that time your average joe certainly did not have an up-to-date smallpox shot--but at multiple border crossings they would hit you up for a bribe if you didn't have an up-to-date smallpox shot. Hence fake them. (Even around 2000 which was the last time I had occasion to have anything added to my yellow book there still was no anti-counterfeit protection.)
It used to depend on where you were coming from. When travelling to Israel for work a few years back, my passport (irish citizen) was not stamped, but my colleague's (at the time, a Turkish citizen) was.
No idea why.