The religious mainline cultural institutions are simply too wealthy to disappear in 300 years, especially if they don't pay taxes. I would assume that they will simply adapt with the times as they always have. I could see world where people consider Islam or Catholicism like we see the Amish today, as outsiders.
I enjoy lifting weights at my home, with no one around. I do it to make sure I don't have to buy new pants. Sports are a good way to tear a ACL.