Some people may have had problems but I never have. With both Bahrain and UAE residence visas I was always cautious when visiting Israel, frequently I did so to get cheap ElAl fares. The Jordanian side did the Allenby crossing with zero hassle on paper as did always Israel. Anybody could have puzzled it out, but nobody ever has bothered me in over twenty years of doing it this way.

I suspect the Israel side cannot hope but see, they look at the other travel. They sometimes make extra screening, I have had some extensive ones, but they are professionals; it is not the TSA. I though the screening was justified.