It's a magical time, and neither of you should have to miss out entirely. The way you are feeling about losing it is the same as your ex feels about missing out too. So I'm sure you can understand some of his pain given your own, and ask him to appreciate you feel that way too.
The usual compromise is xmas eve & day and then swap with the other parent getting xmas evening and boxing day. Or if travel is an issue then boxing day onwards.
It is of course difficult whichever if you are completely excluded, and I do feel for you. Plus doing a hand over on xmas day is never nice. Whoever is collecting has to miss a big chunk of the day with their family regardless, especially if there is any kind of distance involved or you are at grandparents etc.
Is there no way you could see yourself allowing your ex to have xmas lunch with you and opening presents after before he takes the children back to his for boxing day? And then hope that he appreciates it and reciprocates on his year.
Regardless I think it highly unlikely the judge would order every year, and you would certainly have strong grounds to complain in that situation unless there were extenuating circumstances (and even if there were). I assume there is no relevant reason why your ex would never be able to do boxing day (eg work commitments?)
Alternative years is the usual compromise/agreement/enforcement (depending on your viewpoint). And the judge will do everything they can to try and get you to agree to the contact rather than enforce it. So it seems odd that they would insist on you missing xmas eve every year.
Can you accept every other year, given that you get the vast majority of the rest of the year (good times as well as bad) with them. You are after all both of their parents, and really no one 'deserves' it more than the other. Look at it from the children's point of view. I'm sure they would much prefer to have both their parents around on xmas day, assuming they can be civil to one another for a few hours...?