I always have sex while I am on my period. I think it feels a little bit better when I'm on my period. It just seems more sensitive. I don't know if this is in my head or not. I have a very light period due to birth control pills so just a little bit of blood gets on the end of the condom. I've only been active with one person and am very comfortable with it so I like it.
If you're not comfortable with it, or uneasy with it then you don't have to do it. If it's a private thing for you then you most certainly have the right to not have sex while you're on your period. Do whatever makes you happy

Good luck.