If you don't get to the bottom of where his anxieties come from, it might be a red flag that he'll show more of this controlling behavior in other situations.

Personally it wouldn't bother me at all if my SO didn't wear a bra. She would probably go topless at the beach just like lots of other people anyway. Lots of people have breasts and nipples, its not really a big deal.

Maybe his views come from a toxic masculine environment where he believes he has to control his SO. Whatever it is, his boundaries could also cause him a lot of unhappiness and anxiety so a conversation about why exactly he thinks like this will help you make any decisions about your future.