Having an interest in a foreign form media is in fact interest in another countries culture. Something the conservative right doesn't really believe in. Plus, the themes and subjects covered in a lot of animes are really socially left leaning issues. Such as homosexuality and discrimination.
PS. I'm a progressive liberal. :)
For the opposing side, you say that anime promotes homosexuality and liberal ideas, however I think you are wrong. Typically in anime, homosexual content is taken in as a joke, humor, comedy, that is unless you are watching a specifically yaoi or yuri anime. Even so, other common progressive liberal ideologies such as race does not go in their favor. Anime and Japan are very homogeneous in terms of race and how their society runs.
Basically I want things that are effective, and work the way their intended to. Freedom of speech and allowing for political discourse I see as a necessary and fundamental tool which allows us to examine things more closely and improve them as a consequence.
There are plenty of issues examined within anime and to say that one or two are common themes would be reductive at best. A lot of what I've seen is the opposition to unjust treatment (not unfair like a boss being an asshole, unjust as in the state deems your freedoms waived) e.g. Deadman Wonderland, Witch Hunter Robin & Psycho-pass.
I'd argue that the question is poorly written; why not ask what is the most common ideology present within anime or anime fandom? Something that data could be gathered on would be much better for consensus than simply arguing about it.