It seems the Florida - TN rivalry may lessen somewhat with the SEC eliminating divisions. The battle for the SEC east in the 90’s is what set the rivalry in motion. Otherwise, there’s really no natural reason for the two to be rivals.
And frankly, from a Florida fan perspective, we have too many rivalries.
Georgia and FSU are clearly 1a and 1b, and I’d say Miami (even though we don’t play annually) is #3. The hatred between UF-Miami fan bases is way underrated.
Then comes sort of a tie between TN and LSU. Everyone over about 35 thinks TN, people under 35 think LSU. My son is 26 and he’d MUCH prefer beating LSU over TN. Then you even have some sorta weird wannabe rivalries, like UCF, and Kentucky in basketball, and South Carolina wants to be our rival, although we’re just not interested.
So yes, TN is a rival for Florida, but I’d be fine if we could just focus on Ga, FSU and Miami.