It has a lot of far right misinformation, fake news and articles from fishy sites. The mods are biased and wont moderate those.

E.g from yesterday https://www.reddit.com/r/conspiracy/comments/gwgv6i/awfully_...

Sounds like typical conspiracy theory behavior to me, not sure what you expected from a conspiracy subreddit or why you would want the subreddit banned.

Outright falsehoods aren't always conspiracies, they usually lie in the unknowns. It's one thing to say Clinton is a secret Chinese sympathizer, it's another thing to say she was born and brought up in China. Many of the fake news things fall into the latter category, just lies designed to promote the far right.

Conspiracy theories used to more neutral like 5 years ago. Now they're exclusively far right and anti-liberal.

The same thing that's wrong with conspiracy theories (e.g. Q). Lunatics flock to platforms that let them disseminate their lies.

but everything is cleanly tagged under /r/conspiracy ?

Yes and the people who populate that subreddit comment everywhere else, too. Same goes for other misogynist/racist/right-wing subreddits. The proliferation of these subreddits leads to a proliferation of low-quality users.

doesn't reddit have that extension (forget the name) to ban users across all subreddits and tag them etc ? (not from the site but for your own browsing)

You're talking about literally thousands of people you'd need to ban.