I never felt an iota of threat in Jordan and Egypt EXCEPT that when we landed in Aqaba, "they" took our passports, and then it was a very long day. I had left my wallet in our cabin, so I had zero ID. Then, our tour went quite late, and we were more than an hour late getting back to the ship.
I had this fear the ship would depart on time, but as it was a tour provided by the cruise, they waited, and in fact said there were over 100 more people still out. They don't leave without passengers on excursions booked through the cruise line. So, there is that. Otherwise, it was "safe" other than perhaps getting to close to a camel.
This was in Jordan, we got our passports back later and they were already stamped for entry into Egypt before we ported in Egypt. The excursion there was over 8 hour, rather exhausting, long bus rides over uncertain roads to the Nile and back.
Israel at times felt a bit uncomfortable because there were serious looking IDF types in some places, especially inside old Jerusalem. I wouldn't go to Israel today, but this was a year ago. We also stopped in Oman, which also didn't feel at all unsafe.