I grew up gay in the Midwest, so my experience might not match yours if you are used to feeling safe while engaging in public displays of affection. However, I have been in the position of your BF with a (platonic) friend of mine during high school, and in YOUR position with my bf during college.

I hope you will believe me when I say your bf isn't malicious. He is trying to join a new culture and feels unsure of his place in the group. Actively pushing against social barriers is hard enough when you know someone well; being unusual among a group that you want to impress is nerve wracking.

On the other hand, I understand that he is requesting you to consciously change behaviors that are basically unconscious. You are a person with certain mannerisms and trying to "tone down" your personality would be difficult and exhausting and fake.

I think there is a compromise here, but it will require some work from you and some backbone from your bf. It doesn't seem unreasonable for you to edit one mannerism, whatever specific action your BF finds most grating in public. On the other hand, your BF needs to stick up for you verbally, in public any time that you get made fun of where he can hear it.

The basis for this compromise is that your actions are not your personality. If you had developed the habit of popping your gum and it bugged your bf, then it would be a fair concession to try to stop doing that around him. On the other hand, it is unfair for your BF to want you to be someone else entirely. Your BF doesn't get to pick personality traits from a menu... You are an inherently valuable and delightful person who he has developed a relationship with. This "masc dude bro" that he wants you to pretend to be in public isn't the guy he's with. YOU are the guy he's with and if he doesn't want to be with you then that's his problem.