I'm guessing you're not a lawyer, and I'm not either, so there might be some details that are not obvious about it, but the regulation draws the line at allowing you to do[1]:
> any action voluntarily taken in good faith to restrict access to or availability of material that the provider or user considers to be obscene, lewd, lascivious, filthy, excessively violent, harassing, or otherwise objectionable, whether or not such material is constitutionally protected
I think that allows your use case without liability.
That subsection of 230 is about protecting you from being sued for moderating, like being sued by the people who posted the content you took down.
The "my moderation makes me liable for everything I don't moderate" problem, that's what's addressed by the preceding section, the core of the law and the part that's most often at issue, which says that you can't be treated as publisher/speaker of anyone else's content.
It's not a loophole. That's the intended meaning, otherwise it would be a violation of freedom of association.
That doesn't mean anyone is free to promote content without liability, just that moderating by deleting content doesn't make it an "expressive product."
> any action voluntarily taken in good faith to restrict access to or availability of material that the provider or user considers to be obscene, lewd, lascivious, filthy, excessively violent, harassing, or otherwise objectionable, whether or not such material is constitutionally protected
I think that allows your use case without liability.
[1] https://www.law.cornell.edu/uscode/text/47/230