But is there a tactful way in which he could be omitted from the present opening?
Why would you even need to omit him, if your teens didn't have their weird geas about present-opening? It's odd they BOTH have it, but not DD21. They've probably encouraged each other in it, & if you allow it to dictate proceedings, it will become a "Thing", when it really doesn't need to be.
There's nothing intrinsically wrong with the teens' quirk, but using it as a 'reason' (more dark thoughts on this later) to exclude the b/f from part of the traditions of the day is NOT OK. It's THEIR quirk, not his - why should the rest of the household tie itself in knots (you worrying here, DD21 maybe pissed off or inconvenienced) to accommodate it?
They can have their quirk, it would be mean not to take them at their word, even though it's a ridiculous bit of posturing, because they need to know that their feelings are acknowledged & respected. But as it's THEIR decision to brandish private present opening as if it's an innate personality trait, THEY can be the ones to leave the room/house/county/whatever they need to do in order to cope with the trauma of removing wrapping paper from mystery objects.
OK - dark thoughts as threatened promised -
If you were arrange the household so that the teens get to have a 'family only' opening ceremony while b/f is ejected, you'd be allowing them to be precious at the expense of good manners. That's not a wedge you want to get on the thin end of: what next? "Everybody must leave the house because I can't eat my museli when you're here"?
Your teens are playing you. This is a tiny attempt to establish control, possibly in response to DD21 having a fancy French b/f, possibly about something else. I don't think it's a biggie, it's typical teen acting out, but if you indulge it, it could grow like Topsy & you'll be creating the kind of entitled attitude we read about on too many threads here.