Having watched the explosion of Bluesky over the last week, and being on Mastodon for years, I have a different take on it. It's sort of consistent with what you're saying but sort of not.
The problem to me is more that whenever you have a centralized platform that's associated with a single owner, it inherits all the issues of that owner, good and bad. It's inevitable. I'm not sure it's an issue with people not wanting to hear other viewpoints, it's more so people have decided they have had enough of, say, Musk, and don't want to support him. With Facebook stuff came up about that. The other stuff, about feeling like they're drowning in abusive right-wing stuff is also part of it but I think if it were just, say, like the web, they'd say "well this is the web" like people say "this is the news". Once you can point to, say, Musk, and say "he made it this way" or "I don't want to support a person like this", regardless of whether or not it's true or whatever, if enough people feel that way, they're going to want an alternative.
This won't really go away until there's a decentralized open system that's easy to use, and not associated with any given "owner". Mastodon/AP is close but things there are so closely associated with hosts that the host starts to become a dominant issue (see Threads), as does figuring out where to go, and transferability of accounts across servers.
As for "why Bluesky"? Probably because it looks like Twitter and a lot of journalists and politics people were complaining about Threads rules prohibiting things they wanted to post. Not because it's left or right wing, but because of links and political content period. I don't know enough about Threads policies but independently lots of journalists on Bluesky were saying they just couldn't post content on Threads even if it was fairly neutral, or that it wouldn't get any visibility?
Bluesky is easy to sign up for and fairly open. Once you get the journalists and news organizations on there, and a critical mass it grows.
Personally from a technical standpoint I'd like to see Nostr take off but that community currently is very heavily crypto-focused. Network effects and feedback loops are a pain.