It's only the stamp for the Jordanian land border crossing with Israel that triggers some countries' Israel-phobia. Israel will gladly not stamp your passport (for entry or exit) if you ask politely. However, if you have a Jordanian stamp from that land crossing, the only way to have gotten it was to be coming from Israel into Jordan. Therefore, they have proof that you were in Israel. I have no idea if the Jordanian authorities will skip out on stamping your passport there if you request it.