That is kind of annoying, and you're right, unless the show is about politics (like Spin City), you really don't need to engage in something so polarizing. Kelsey Grammar is really right-wing, but Frasier is very neutral. They only got into politics a few times on the show, and even then it was restricted to stories about fictional characters that were directly looking for Crane support or feedback. On the Simpsons, Sideshow Bob ran for Mayor as a Republican, but that wasn't nearly as important as the fact that he's just a villain.
Honestly, Last Man Standing didn't really do anything for me, which kinda sucks because I like Tim Allen and I dug Home Improvement, and they definitely tried to put similar elements into this project, but... it didn't click. Lightning doesn't always strike twice.