Parents and their children will embarrass each other for the whole of their lifetimes. Choose ANY subject and their will be disagreement at some level between the generations.

If it were me, I would use it as a learning experience (maybe a whole family learning experience). Being tolerant of other's choices is something to be admired. And your daughter is going to make some choices in the next 10 years that will turn your hair grey overnight.

Regards

Chas