Many Israelis are known to fly Royal Jordanian, as they offer cheaper flights to south-east Asia, where as El Al is very expensive, and takes longer flights paths, as to avoid flying over hostile countries.
Flying Royal Jordanian might feel awkward, as it mostly serves passengers transiting to various
Arab countries. I hear the terminal there is also quite shabby, although a brand new terminal is
supposed to open up very shortly.
Amman is a stones throw from Jerusalem, and Palestinians who do not hold Israeli passports, are prohibited from flying out from Ben Gurion and fly out from Amman instead.