You betcha they do!
You went off topic, not surprising. It’s not about anyone wearing hats - that was never the issue. No one is saying the mad hatter should stop wearing hats. She takes it off when the rules apply. Not to difficult to do or ask to be done.
TOO much time wasted on someone else’s hangups.
And do you fault her for wanting to change the rules? When the rule was instituted, there were no women congressmen. It was a rule that applied only to men.
The tradition of women wearing hats indoors goes back to Biblical times. It is a sign of modesty (believe it or not) and the fact that this woman wants to change a rule so that women can be more like women, should encourage "conservatives" rather than ruffle their feathers.
I say more power to her on this issue. This is a fashion issue and not a political one. Cut her some slack. I personally admire her individuality although I detest her politics.