Does any of your characters consider another character as a rival?
Yes, one of my characters has several rivals. My other character used to have some but they left the realm.
Aramon Abjur vs. Innocent Noble was the biggest feud I was ever involved in.
Depends a bit on your terminology of rival.
I mean the fued between Garas and Ecthelion is huge, but is it a rivalry?
Other than that my infil has a bit of a rivalry to see who's the best infil and those sort of things.