I grew up in L.A. (Lynwood, just north of Compton and just east of Watts) and lived in the Ozarks in southwest Missouri for some time as an adult, so I'm just going to claim a bit of "been there" status in replying here.
I had cousins who knew people up in the area between Lebanon and Rolla, in some really backwoods places, who regularly hunted squirrel, shot dove and other fowl, and fished for dinner fairly often, but who also had regular jobs and could go into town to the grocery store anytime. It really wasn't a matter of being hick or rube or anything else. It was just a cultural thing, and they were proud of it. Cable TV, college football, and CNN -- and squirrel. Not even kidding.
I would imagine that may be less true since the advent of the internet and the tendency for regional cultures to get homogenized, although I haven't been up there much since that came about, so I definitely could be wrong.
I also lived in Springfield for about four years, a medium-sized city with a fairly large university and several small colleges, a thriving culture-and-arts center, and various other aspects of non-stereotypical-hillbilly life. And yet, you could drive 10 minutes away from town in pretty much any direction and you'd be in what felt like backwoods. You'd be around people who had small farms, or who even hunted and fished for at least some of their food, put up food for the winter, etc., and yet would go into town all the time to go to the mall, or for some big production at the university, or whatever the latest Tom Hanks movie was.
I guess what I'm saying is, there really isn't anything particularly odd about the Clampetts living near a town that had stores, a town square, a theater, etc., and still having a backwoods kind of existence. Obviously it's made cartoonish in the sitcom genre here, and maybe that's exactly the point. In reality, given the kind of people who would actually be more or less like them, there wouldn't be a conflict. But it's probably legit to say there was a conflict specifically because the "rube" side of their backstory was such an extreme caricature.
What I find odd was Granny, in ALL of her years of living had never seen a helicopter or airplane fly over...in the pilot episode she thought the helicopter was a big bird.
Also It's hard to believe the Clampetts had never heard of Halloween.
What I thought odd though about the change is history was, in the color episodes the Clampetts talked about GOING to all these places back home, like to the town square, the theater, having a party line phone, etc... BUT when they first moved to Beverly Hills they acted like they had no clue what any of those things are.
Yup, it's a good point.
Somebody should do a short book or a TV special about all the times sitcoms simply ignored their own established backstory and storylines. You have all kinds of instances where writers just acted like something never happened at all, characters (even family members) that disappeared entirely, etc.
In a broad-comedy show that plays on stereotypes like TBH, that kind of thing is bound to show in exactly the kinds of aspects you've outlined here.
From a comedy stand-point, I guess in the early episodes they had to portray the Clampetts as being from a world totally different from Beverlly Hills.. BUT as the show went on, they felt they kinda had to change the Clampett's backstory to match the present day happenings a little bit.