Fogerty's accent has to be contrived. He grew up in El Cerrito, one town over from Berkeley, and speaks in a normal California accent. The weird accent only appears on some songs, Proud Mary, Green Rivah, Born on the Bayou, Keep on Chooglin, etc. Great music for sure.

Concerning Dylan, I think he tried to cultivate an Okie accent due to his admiration for Woody. It is a small matter considering his genius as a writer.