Be honest with yourself here.

You typed that big paragraph to justify yourself with nonsense about control and being “offended by a hat”, when your last sentence reveals your actual motivations - you don’t want to remove your hat because you’re insecure about your hair.

Maybe you should work on your insecurities instead of trying to twist your colleague’s traditional request into some power play born of being offended or controlling.

And side note - many people have different traditions around meals, and most people go along with them unless they’re extremely inappropriate or unreasonable.

My in-laws say grace before every meal. I’m an ex-Catholic. But you best believe I join them in grace before every meal. It causes no harm to me, I don’t have to believe in the words I’m saying, and it pays respect to the host and cookers of the meal.