Middle East travel

I’m thinking of doing some travel after the election, and one option is to go to the Middle East, or specifically Turkey, Egypt and Israel as they’re countries I’ve never been to with huge historic monuments etc.

I sort of recall that in the past if you went to Israel, you might have problem getting into other Middle East countries, so one should have a second passport just for Israel, or alternatively visit there last.

Does anyone from from recent experience if this is still the case?

I’m not 100% definite on the destination.  Also want to do a trip through Talinn,  Helsinki, Auschwitz, Vienna and Berlin.  Will decide closer to the time.