(Ash mentioned! <3) Endorsed, I think this nails his place on the spectrum of politics in multiple ways. I will toss in a few thoughts:
-- I am on the record somewhere as a "liberal Gunbuster" truther, so no surprise here from me, but yeah I think the Gunbuster case tends to be overblown and is imo the source for most of the "right wing" discourse. It's a bit tough for westerners to see the ways Japan sees WW2; apocalyptic in outcome but typical in stakes. Using iconography from Ghengis Khan or Napoleon is fine for us, because while awful human beings it was in that typical "war is always awful" way, it isn't a poisoned well. WW2 is not that for us, but the typical Japanese person is likely to see it through that kind of lens.
As such all the Gunbuster homages to the Battle of Okinawa, Japan annexing Hawaii, etc, are all just the touches of the genre of Space Opera and military otaku things. Putting a space lesbian in a steampunk Napoleon uniform a la modern YA books doesn't imply the author endorses the Confederation of the Rhine or anything; and meanwhile Gunbuster's actual setting is UN-on-Steroids international liberalism, it is not apologia for the East Asian Co-Prosperity Sphere. The imagery just doesn't carry the same implications.
(IMO this perception of WW2 is wrong, Japan was in fact atypically awful? And this is tied up with a whole bunch of cultural-political stuff in Japan. But Anno/Gainax as creators aren't water-carriers for all of that, just downstream of it)
-- Anno is definitely in that post-Anpo "apolitical otaku" generation, but I think if you move a bit past the left-right binary you can find a lot of politics in there. They are in a way "anti-left" in the sense of wanting to remove what they see as overbearing political content from media, but it isn't just so they can play with their toys in peace. Anno has lost faith in politics as a solution to societal problems:
--In Gundam, the main character, Amuro Ray, has a clear enemy and a clear political structure that encourages his growth, but "Eva" doesn't have that.
Anno: From a generational point of view, I myself don't have that concept anymore. I don't trust politics or society. I can't create works that adopt what is not there.
(Interview: STUDIO VOICE October 1996)
“…For [my generation, after the political failures of the previous], there was nothing to speak of but what was within the ‘magic box’ (television). It’s pathetic, but we had no other options. I think admitting that is a start.”
(A Dream World That Hasn't Forfeited its Goal, ~August 1996)
And you see more of this whenever he discusses things like the Aum Shinrikyo cult/Tokyo Sarin Gas attacks (which occurred during the airing of Eva); he will see them as case of extreme involution, obsession with the self & disconnected from society; a problem that political orgs are now incapable of fixing or addressing. And otaku are a calmer-but-still-troubled side of that same coin, a response to capital-M Modernity. That is a deeply political stance, right? It just isn't one that lends itself to voting for this or that party.
This was a pretty big ~vibe in the 90's all over, honestly, and at the time I would say it was still pretty left coded? But it had its sources on the right as well (horseshoe theory continuing to bat a hundred), and fell out of favor in the West at least - idk maybe something happened in American in the 2000's to distract from the ennui, couldn't say. It lasted longer in Japan, and I think you can trace an arc from many anime creators being actively political in the 1970's/1980's, to a new gen being intentionally anti-political as its own politics in the 1980's-1990's, to anime being dominated by truly apolitical creators starting in the 2000's. Anno is part of that middle wave. But it is all by degrees of course.
-- Finally; Anno is in his mid-60's, his politics have changed! He definitely doesn't discuss them that much - but like you can't look at Shin Godzilla and say "yeah this guy has no thoughts on the Fukushima Nuclear Disaster", its a film clearly dealing with the bureaucratic limitations of any system being able to "contain" the mess of reality. He didn't have those opinions before because Fukushima hadn't happened.
I know this one quote from these rountables Anno did with a bunch of high school students during the production of Kare Kano? Which, btw, were printed with this logo:
"Anno Hideaki X Highschool Boys & Girls" lovely, 10 out of 10, no notes. But anyway, he goes off at one point about the US & Japan and international relations.
Anno: Asia is where it’s at now. We’d best get in good with our neighbors. The previous generation is with America. Those currently in their 50’s typically think in terms of America. In reaction to losing the War to America, they all want to live the American lifestyle. Like all going to Europe, that sort of thing.
And idk I bet that the past 20+ years of declining relations with and rising bellicosity from China has soured him on this! I don't have a money quote, but i'd be shocked if he stands by this off-hand comment from the 90's. People do this a lot, you see an interview with someone, they say something, Miyazaki will tell you Humanity is Doomed or some shit, and that becomes their canon opinion. Which is understandable because it's printed, but maybe they were just shooting the shit, and maybe they believed for ~5 years or something. Maybe they never believed it, who knows right? They are artists, not politicians or academics, so they aren't normally in the business of making their political evolutions robustly explicit. And this generation of creators in Japan loved to run their mouths.
So I think, like many people, you can't say Anno over the course of ~50 years of having opinions on politics, is going to fit on one side or the other that neatly.
--- How many Left Points does Anno get for making fujoshi gayboy flagship Kaworu and leaning into that so goddamn hard in the mid 90's? Guy did a 30-page interview for JUNE, the oldest yaoi magazine around! That has to get you at least 10 Ikuhara-blazoned gold stars right?