I also share a birthday with my FIL. Somehow this has never been an issue. Your boyfriend and your mom even have different birthdays. I don’t think you’re making him feel like both of their birthdays have the same priority because you leave his birthday early to start celebrating your mom’s birthday, which hasn’t even started by this point.

Does this happen for anyone else’s birthday too or just your moms?

But should it though? If they end up getting married, he becomes her immediate family and should have reasonable priority over her parents. I believe setting boundaries with parents/in-laws is better done sooner than later.

I don’t see why you need to be there the night of your moms birthday? If the trip is until the first then you’ll still get home at some point on her birthday and can celebrate with her?