Why was Humphrey Teague trying to suppress worship of the Old Gods. Shouldn’t the Blackwoods have been the only ones left south of the Neck by that point? And why would the Tullys and Vances have supported the Blackwoods given that they are followers of the Seven?

The Blackwoods are the only highborn house that we know of, there could be more and there could be smallfolk who follow the Old Gods no matter what their lords say. 

As for the Tullys and Vances, they likely had other motives. The Vances had warred against House Teague for the crown of the Riverlands in the past, and the Tullys were vassals of the Vances.