I wouldn't mind it, honestly. I can definitely understand if a few accessories that other people wear may come off as distracting or rude to some, but it's just a cap, in my opinion, so I wouldn't worry too much about it.

I don't have a problem with it. I wouldn't appreciate it if someone told me to take my hat or cap off if I had one on either. But I think for some people, a hat or cap could be distracting, so I can understand to that extent. Beyond that, I don't think anyone has the right to tell or even ask people not to wear what they are comfortable in.

You are your own person and you can wear whatever makes you feel comfortable as long as it doesn't distract you or the teacher.But ,most importantly it should not be the focus of the lesson... Yes ,that is the Spirit, laughing at certain situations help lighten the mood.

A cap, and I'm thinking of a baseball cap, would be worn by someone who is using it hide themselves to some degree. It is representative then of nervousness or anxiety in the wearer when that is in the context of a classroom online or offline. It makes them feel protected. It is my job as a teacher to make the student feel comfortable and confident, so that the cap is no longer required. Although it may be that the cap is hiding them from someone or something else, not the teacher. I wouldn't ask a student to take it off, or do anything that made them feel uncomfortable. If a teacher, on the other hand is wearing a cap in a lesson other than as realia or a prop, then as a student I would be concerned.

Maybe someone might have a very personal reason for feeling more comfortable wearing a cap.