Just flew TLV-AMM-DXB last week. No issues in DXB at all. Israel does not stamp passports at airport and has not for some years. and no issues in Israel either.. there is no reason to think this is a bad time to visit. The Jordanians are concerned about the drop in tourism, which they blamed on bad press.

While Israel is aware of what neighboring countries may think about people who have been to Israel, I dont think that was the motivation to go to their new system .its was a new system developed. you always had the option to not have your passport stamped, now there is just no option.