Is it still unacceptable to wear a hat indoors?

I know this will probably sound stupid, but I'm clearly not a hat wearer.

I have never really work hats before, but I wore one today when I went to the park to workout. I was going to stop at the library on my way home to grab some movies, but wasn't sure if I should wear my hat or not. I didn't want to take it off because I had the hat lime across my forehead, but I didn't want to wear it and be rude.

I just went home instead and I'll go to the library later.