We don't have "processes" at HN. The idea makes my skin crawl.
Plenty of both left- and right-wing sites are banned and/or downweighted on HN. When a site is primarily about political battle, we either ban it or downweight it. Which of the two we choose depends on how likely the site is to produce the occasional interesting article (in HN's sense of the word "interesting"). That's why The Federalist and World Workers Daily (or whatever it's called) are banned, while National Review and Jacobin are merely downweighted. Both the Guardian and Daily Beast are downweighted, btw, as are most major media sites.
If you or anyone thinks that HN moderation is unfairly ideologically biased, I'm open to the critique, but you guys need to first look at the site as it actually is, and not just look at your own pre-existing perceptions. Every data point becomes a Convincing Proof when you do the latter.
People think that when their team gets moderated, the mods are OMG obviously on the other side. The Other Side feels exactly the same way. This "they're against me" perception is the most reliable phenomenon I've observed on HN. Leftists feel it, rightists feel it, Go programmers feel it, even Rust programmers feel it. Literally the very-most-popular topic on HN at any moment is perceived by someone as Viciously Suppressed because of this perception. Stop and think about that—it's kind of amazing. Someone should write a PhD thesis.