So what? You're taking it as a given that "if a website moderates content in a way I don't like, the government must step in and force them to do moderation in a different way I do like"; I don't accept that premise at all, it's quite totalitarian in both concept and real-world execution.
So what? And I mean that quite seriously.
To clarify, I despise the big social media platforms and refuse to use them even if that inconveniences me (and occasionally it does). At the same time, those platforms have the same free speech rights that I do, and curtailment of their free speech (and property) rights (in this case, the right not to publish/amplify the speech of others) also curtails my free speech (and property) rights.
And since I want to protect my own rights, I support the right of those rapacious scumbags to moderate/censor on their own private property.
So, for example if libel against you wasn't caught by a particular filter then that's not bias against you, and so they are not party to the libel (unless you can show the filter was specifically designed to fail to catch libels against you).
It's all politics and it always was. Claiming one is "common sense" and one is "political" misses what "political" means.
I think S230 set a pretty good tone in biasing in favor of the right of the service owner to set the tone over-and-above within the constraints of the law (for a simple practical reason: if you don't give them that right, they'll just stop providing the service). But that does mean that when your provider decides that, say, debating the humanity of trans folks is no longer acceptable, we toe the line there or we start our own service.
If a friend invited me to their house I can start calling their wife a fat cow and tell them how ugly I think their children are. It doesn't mean they have to put up with it or accept that sort of speech on their private property. That doesn't mean he censored me or inhibited my freedom of speech.
For me, it's an issue of scale. Your friend is a single person (or family). Twitter is a gigantic, faceless corporation (okay, Elon Musk makes it less faceless, but you know what I mean) that tries to cater to everyone—in effect, it tries to be a commons. Can we consider it one? Should we? Should we make a law that says once a social media company gets to a certain size, it can't censor anything anymore if that content is legal?
I'm generally against additional regulation. I don't think, for instance, a small pro-life forum should be forced to allow pro-choice people to spew vitriol, nor vice versa. I'm hesitant to say the same for a giant company like Twitter or Facebook. There, I think it might be more appropriate to have comprehensive filtering and self-moderation tools vs. shutting people out completely (assuming their behavior is legal).
My statements, while I myself do not necessarily agree with them, are what I view as possible when operating within the current legal framework our government has built for these private companies.
To me, if the government wants to hold a private company to the standard of a public service, then that private company must fully, legally, and entirely become (somewhat) a public service. I view that as becoming a service similar to the United States Post Office.
It's allowed to continue to operate as a company but has to comply with government regulations (whatever those may be). That also means that its goal is not profit generation. It can still charge users for certain services if it wishes but is no longer able to sell user data, and it must remain revenue-neutral.
But the solution to this problem is not to force those private service providers to be hands-off, but to make sure that none of them are big enough that it matters. Which the political forces that are pushing for these laws won't do, because their political economy boils down to "capitalism good, anti-monopoly bad", and that inevitably leads to the present state of affairs in practice.
Let me be very clear about how the law would work sans CDA 230: any time someone does not like what you are saying, they can sue the platform you host it on to get you censored. The only platforms resistant to this would be ones full to bursting with spam. This is already really bad. If you want a partial repeal, i.e. one where platforms are still allowed to "protect minors from child predators", I'm not sure that'll pass muster at SCOTUS. Selectively removing speech protections based on content is a no-go.
Furthermore, platforms being able to take down political speech they disagree with is not a "loophole". That's just what moderation is. The whole point of a moderator is to silence the loudest voices, so that others may speak.
If you want to allow the kind of private censorship S230 was intended to protect, and stay within the First Amendment, S230 is what you get.