Daisy

When you enter Isreal you can request for your passport not to get stamped for work purposes, it's worth doing and saves a lot of hassle in other countries.

You might get an 'interview' by the Isreali boarder control, I've found it not to be a problem.
Other option worth considering: 2nd passport, always handy.

And ot answer your question directly: it could be hard to enter ANY Middle Eastern Country with an Isreali stamp in your passport, not impossible, but harder and sometimes it can mean anything from: visas get delayed, not validated or revoced.