Do you want a value answer or legal one?
The legal answer is that we have narrow exceptions to freedom of association around businesses (and a few other places) refusing service and closing doors to very specific protected classifications. Arguably they should be a little less narrow, but that's straying into a values answer. Of the attributes you list, race and gender are pretty strong protected categories. Age to a lesser degree. Marxism is a political category, there is no law that says Twitter couldn't ban someone for being Marxist.
These are very narrow categories, and for most part anything outside of them is fair game.
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From a values perspective, I think our current system is pretty good.
We don't restrict the ability to ban users except in very specific cases for very specific protected categories. Those categories are narrowly defined, based on strong needs that communities have for protection. We can expand those protections of course, but the fact that we have very narrow exceptions to users' Right to Filter[0] in narrow situations does not mean that we should ditch the entire thing. Just because your content is technically legal does not mean you have a right to force me to consume it.
In other words, I'm quite sympathetic to the argument that our protected categories should be broader in some instances. I'm not sympathetic to the argument that because protected categories exist, a forum shouldn't be able to ban Republicans or Democrats. If you want to take away a community's Right to Filter on an attribute, I believe you should be required to demonstrate an extremely clear, compelling need to protect that specific attribute.
And in particular, I don't see any reason at all to expand those protections to political categories.
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While we're on the subject of laws, it's always important to remind people that in the US, hate speech is protected speech -- and that's probably not going to change any time in the near future. The Supreme Court has been remarkably consistent on this point for a pretty long time.
This has implications for what revoking section 230 means.
Before section 230, the Supreme Court ruled that platforms that had no knowledge of the content on their site -- that were not moderating it in any way -- couldn't be constitutionally held liable for speech on their platform[1]. Absent 230, if Facebook wants to call itself a platform, it needs to fall back on that ruling. So if they see someone harassing you for being Jewish, or female, or Marxist, or older than 40, Facebook won't be able to ban that person. Engaging in any moderation will make them liable for all of the content posted on their site. And no company-run corporate platform is going to risk personal liability for all of their content just to ban nazis.
Given that reality, I don't think any progressive should be arguing for the removal of section 230. Using a legal standard for moderation will make the Internet way more toxic for underrepresented groups than it already is today.
I have heard people (usually non-progressives) make the argument that this is fine, because if no one is banned from any community, everyone can participate. In other words, let the trolls run wild. I don't have much respect for that argument. If you allow every open forum to become toxic, only toxic people will be able to stomach them. Safe spaces foster diversity, and there is no way to build a safe space for user-generated content without moderation. If you don't believe me, then go join 8Chan and have fun, I guess.
I know a few progressives are hoping that the user-generated content will go away entirely, and that Jewish/female/Marxist/middle-aged people will just participate on traditional channels. I think this is also kind of naive. No one who's seriously looked at the history of traditional media channels would come away thinking they've been bastions of the progressive movement. Marginalized voices have been excluded from those channels again and again, and it's only by fighting, by circumvention, and by self-publishing their own stories and building their own collectives and communities that those marginalized voices have been able to make themselves heard.
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[0]: https://anewdigitalmanifesto.com/#right-to-filter
[1]: https://en.wikipedia.org/wiki/Section_230_of_the_Communicati...