Politics kinda depends on varying parties holding power relative to you and then you dealing with them in a fashion other than warfare because it's hurtful to yourself to do otherwise. I mean, come on, you have 2 or 3 Goddesses living in the house. They can blink their eyes and make the universe disappear, it makes the politics an unnecessary indulgence - kinda like a housecat meowing for something and you "negotiating" with it. Regardless of the cat's actions, a person is going to do whatever they feel like with the cat to begin with (kick it, feed it, ignore it) and the same with a goddess towards people.

Does anyone take TM!R politics seriously?

What aspect do you like about it specifically? And what areas (royal houses, etcetera)?

Despite having an interest in politics in reality, I never really cared for the politics in Tenchi. It isn't that they're poorly done, I just prefer the show without it. The whole arranged marriage thing with Noike and Tenchi being an heir to the Juraian throne just felt out of place to me. I thought the show did things best without politics (Back in the second and even first OVAs). I truly felt the show had enough charm that the addition of an empire wasn't really needed. It almost feels like they're trying to scale it up just for the sake of doing so. I can almost compare the way original Tenchi feels to Ah My Goddess. Both shows generally keep scale small (just within their circle's of friends), and limit outside character interaction. But suddenly, OVA3 (I'll refrain from mega-ranting but OVA3 was the best example of Jurai's politics at work) decided to plop that in and change the family/band of friends dynamic that they had going for it. I'll admit, some of it intrigues me (mostly cultural differences), but generally it's like eating right after brushing ones teeth, it leaves a bad taste in your mouth.

Its been shown that the show can easily survive without it, I mean look at the first 2 OVA's, the politics werent even really around till the very end of OVA2 and the series afterwords, which just made things way too complicated and took away from the show, Tenchi is a simple man, his show should also be simple like it was

I have no problem with there being politics in Tenchi Muyo.
However, the politics should stay in the background, and not take up the shows main story(which should be centered on Tenchi and the girls).
I like the way that Tenchi Universe handled politics(there was a conspiracy going on on planet Jurai, that the characters had to figure out to clear there names) in a way that did not undermine the whole story.

I've always found the politics of the OVA boring. I agree with Tenchiman, I liked the way they handled it in Universe better. In Universe the politics were relevant to the series. I'm still not sure why the OVA brought politics into the series because it just felt forced and was sleep inducing.