Even entering Israel can be tough...I have had to sit and explain why I have entries and exits from Jordan in my passport from years earlier. All were work related and she eventually warmed up to it...but still, make it as easy as possible.
Really? I find that surprising, especially since Jordan and Israel have an open border with each other. Israelis and Jordanians viewed each other longingly for years across the border, and when they finally opened the border in the 90's citizens from both sides poured in. (The border is also open with Egypt, but the travel seems very one sided-- Israelis visit Egypt but Egyptians are disuaded from visiting Israel, illustrating that the Israeli-Egyptian peace is very one sided.)
In January I had the following conversation with the Passport Control agent at Ben Gurion airport:
Passport Control Agent: Baruchim Haba'im. Welcome to Israel.
Me: Thank you. May I ask a question. Next month I plan to visit Dubai for a job interview. Will I have a problem the next time I come to Israel.
PCA: No, of course not. Why would you have a problem?
Me: Umm... Because I will have a stamp from an Arab country that does not have diplomatic relations with Israel?
PCA: So? We have many people with Arab stamps in their passport. Especially with Dubai, UAE there will not be a problem. Some Israeli businessmen travel to the UAE, and they have no problem there and they have no problem here.
Me: Really? They let Israelis in? I thought they didn't recognize Israel.
PCA: Well, they recognize the money the businessmen bring. For business the sometimes forget they hate us.
Me: Okay, thank you very much.
PCA: Enjoy your visit Mr. XXXX. L'hitra'ot Shalom, XXXXX (to my 4-year-old).