You've heard this accusation before; heck it occupies 90% of the YMMV section of the article, but it rings true to me, so much so that it cannot be said enough; somewhere along King of the Hill's 13 season run, the fine balance between characterization and comedy was disrupted for worse.
When KOTH first started out, it excelled in playing Texas stereotypes against realistic behaviors. As the series progressed, the stereotypes were dialed up slowly but surely but were always counterbalanced by a episode dedicated to bringing back the relatability. This could be in an number of ways, be it by a new face to flesh out others, having mostly right heroes be dead wrong and vice versa, and most importantly, FOR ALL OF IT TO BE RECOGNIZED IN UNIVERSE.
Somewhere along the lines the writers caught whatever the Simpsons writers had that made them lose that respect for whomever wasn't the Creator's Pet (looking at you Lisa) and let the exaggerations seep in more. Episodes stopped being subtly complex stories told in a humorous way to obvious good vs evil idiot plots. Or rather, Hank Hill vs Whomever he didn't like that week.
Now, this really has nothing to do with behaviors and beliefs present within the Texas community, but rather that each and every dissenter was an axe-crazy strawman that would stop at nothing to bring down the community of Arlen, leaving the infallible Hank Hill to step in and set things right.
But this craziness didn't come and go with the one-shot characters and the small number of returning antagonists, no sir; even family members and friends would be swept up in it, turning once multilayered characters meant to represent different types of people into nutjob pinheads defined by nothing but their wacky hijinks. After all, Hank needs some kind of conflict to be the designated hero, and lord knows he can't be wrong when it really matters.
Perhaps it was a blessing in disguise that KOTH died before any further damage could be done. After all, when your series finale ends the shaky father-son dynamic by having Hank finally accepting his son NOT as who he is, but by Bobby becoming what he wished him to be (through some contrived bullshit), then you know your series is just that.