I read the entirety of the page you linked to. Nowhere I found does it say that neutrality is required for the protection to apply, nor that pre-approval or vetting copyright would waive the protection, nor that the protection is in exchange for supporting free speech. Could you point that out to me?
In fact, it links to another page which states:
Wow, is there anything Section 230 can't do?
Yes. It does not apply to [...] intellectual property law
Which directly contradicts your implication that Section 230 is the law that grandparent was referring to when they stated:
The government [...] granted [internet services] immunity
to copyright related suits [...] (This is a law.)
Furthermore, Section 230 explicitly states that its liability protection DOESN'T require neutrality, and extends to:
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
Sure, but it (1) doesn't apply to copyright—that's the DMCA safe harbor not the CDA one, and (2) was specifically created to eliminate the added liability web hosts were then subject to if they engaged in content moderation, not to require them to abstain from moderation to secure the safe harbor.
