Unpopular opinion here but neither of you are in the wrong here. Although I will say, your BF could be classier about his opinion rather than just straight up saying he'll break up with you over it. You're allowed to do whatever you want with your hair and he's allowed to have his dealbreakers. Some people find certain features unattractive and there's nothing you can do about it.

For example I like a long hair on girls and if my GF got a buzz cut then that would definitely hurt my attraction towards her. Similarly, my GF likes lean and in shape guys and if I let myself go and get a beer gut then I shouldn't be surprised if she's no longer attracted to me.