I think you flipped a right/left handed towards the end, but I follow what you're trying to say. The thing is most don't believe in a right where everyone has to listen to anything said with equal opportunity. It definitely is a tyranny of the majority, but that doesn't mean a tyranny of the minority, where anything said should get equal exposure regardless of how unpopular it is, is inherently more correct, or necessarily better.

That's why "The hard part is convincing others what you want to say is what they want to see here." It's not that they need to read everything, it's that they need to see those things they typically want to ignore as something worth them spending time on. No amount of moderation will make people spend time reading things they aren't interested in reading. Part of this is you end up with communities with different focus, and that's usually the way these kinds of differences co-exist in the same world at scale. Once the communities get large enough, they are in some way forced to find neutral ways to interact. Typically this happens more in the real world than on the internet.

The only time this really breaks is when the divider isn't related to content, rather some arbitrary attribute unrelated to it. E.g. if a conversation about the best quality paints ignores someone because of their handedness. The content of what they were saying had nothing to do with the exclusion so people want to protect against those kind of exclusions. The same feeling does not extend to those that want to bring a content reason for exclusion into the conversation, e.g. someone that constantly talks about how paint is a conspiracy by $BigCorp and can't talk about paint without always bringing it up. In that case the person needs to find people interested in talking about $BigCorp paint conspiracies, not a moderator to force people to listen to them.