Blood-blood contact is a big risk for ANY kind of infection or disease. But the penis is covered in skin. It's advisable for the man (and woman) to urinate after sex to minimise the risk of a urinary tract infection anyway, because the mucous membranes of the vagina can be a source of infection regardless of menstruation.
If it's the man bleeding, of course, that's blood in contact with someone else's mucous membrane and is an infection risk.
In other words:
If you're going to get an STD from sex during menstruation, you must be doing it unprotected. You get infections from unprotected sex anyway!