I ran cross country and track and field with no trouble while wearing normal prescription glasses, as did several friends. I wear my glasses fairly snug, but unfortunately everyone's ear and face shape is odd in their own ways, so it might not be possible to get a secure fit that is also comfortable.
Worst case scenario: Companies make what are essentially prescription goggles, like you can see in the NBA
Worst case scenario: Companies make what are essentially prescription goggles, like you can see in the NBA