Oh come on! This is getting too much! Her b/f is Muslim. They met at Uni, they both done computer science degrees. He's a lovely caring young man and if anything my daughter bosses him around!
Now I do have to ask:
How long have DD and BF been together? They are living together?
Was BF not invited? Was BF explicitely uninvited?
Although Christmas is a Christian holiday celebrating the birth of Jesus Christ, coinciding with what used to be the pagan Juletide (midwinter) festival, most people/families do not really celebrate the religious part. For most people Christmas is about being with family. As is Eid, Hanuka or Thanksgiving.
Your post does not make it clear, whether he would like to join in, whether he rejects Christmas and all things Christian, how your daughter feels about it ... She doesn't seem to want to leave him alone on the day, which suggests Christmas, family, people close to her, are important to her.
In my family, I would expect DD's BF to join in the Xmas get-together, and I would expect DD join in his family's Eid get-together. A traditional turkey should be no problem for a Muslim, leave away any bacon and pork (no harm in that), maybe even go the extra mile and get a halal turkey. If you do say grace at the dinner table I would of course not expect him to join in. If you have bubbly, get some alcohol-free as an option. That should have most bases covered, maybe just in case ask your DD.
If your family cannot navigate Xmas with BF, how is the future going work out? Not ever have Xmas with DD again? Although you say he is a lovely caring young man, are you (and DH) are really taking the relationship seriously? Or hoping it will fizzle out, and you are not really welcoming BF into family? What is DHs attitude toward BF?
This seems like opening up another can of worms, but maybe it is just another aspect/symptom what going wrong in your marriage/life, making you unhappy. Something to think about...