Actually... king of the hill isnt that conservative. They sort of parody him as having to be conservative because of who he is and where he lives but the shows messaging is overall very liberal. They completely ignore many current events that happened at that time and would have been relevant.

The only things I can say come around as "conservative" are the facts that Hank is hard working and self sufficient as possible.... but they go as far as to still insert their messaging (as far as it was being pushed everywhere else at the same time) as much as any other show of the time. The simpsons could also be seen equally as "conservative" for its time, and poked fun at communism for instance quite a lot. But if made today... King of the hill would probably be pretty bad.