Hola Mary /
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Being Jewish should not be a problem in DXB, and all the answers and recommendations by our friends here are correct. Of all the Middle East area, the DXB Emirate is business oriented, and should be OK for you.
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But if you fly to/from some countries around there, be careful. As an example, in Saudi Arabia. I have worked a long time for an ACMI with SV, and was based in JED, and I even knew 2 captains who were Jewish, and worked for SV... but they listed theirselves as "Christian" on their documents.
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Funny is, once shopping for gold jewellery in JED in the gold souk there, the shop keeper showed me little Christian crosses and crucifixes for sale, that he kept hidden behind his desk. Smiling, I asked him if he had "Stars of David" as well for sale, he smiled at me, but did not answer. And the diamonds he was selling were probably coming from the Antwerp Jewish diamond market.
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Another time, we needed maintenance on our 747, fully painted in SV colours and names, and for whatever reason, the company contracted BEDEK Aviation in TLV to do the job, so we flew out of JED, with a flight plan to Larnaca, Cyprus, and from there we flew to TLV. Same thing on the way back. Must have been a curiosity for "aircraft spotters" to see a Saudia 747 parked on Tel Aviv airport...
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Like everyone says here, do not say anything. If your name is Yiddish, just tell them your ancestry is Germanic if they ask you. If you visit Israel, be careful not to get your passport stamped by the Israelis, ask them to stamp your entry/exit on a page that is stapled to a page of your passport.
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Shalom
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Happy contrails