Sheldon’s father has been mentioned as an alcoholic, Leonard’s father has been mentioned, as a plotline in an earlier season was his mother telling him that they were getting divorced. I always got the impression Howard’s dad was deceased and Penny’s dad was on a couple episodes, and he’s portrayed as a common sense country boy.
Or at least a heavy drinker. I've gotten the impression he was more a stereotypical Texas redneck than anything else. And while he is deceased, it appears it was only shortly before the show began, since Sheldon's sister visited with legal paperwork to do with his estate. So he died when Sheldon was an adult, which is nothing unusual for any family.
Sheldon's mother is a Christian, and despite her occasional eccentricities, she is portrayed as a voice of reason—she's the "nuclear option" that Sheldon's friends will fly in to talk him out of something really stupid. In other words, Sheldon's family is not dysfunctional. He's the odd one.
Leonard’s father has been mentioned, as a plotline in an earlier season was his mother telling him that they were getting divorced.
Leonard's family are all highly motivated academics; their dysfunction is played up for laughs.
I always got the impression Howard’s dad was deceased and Penny’s dad was on a couple episodes, and he’s portrayed as a common sense country boy.
Howard's dad actually left. Apart from that, his mother is an over-the-top stereotypical Jewish mother; again, their relationship is played for laughs. And, as you point out, Penny's dad is a regular good ol' boy, and Penny is just a girl from the Corn Belt trying to make it in California.
I find it hard to maintain an argument that The Big Bang Theory is part of a broader agenda to normalize non-traditional families. It's a program about socially awkward nerds. Everyone's an exaggerated oddball.