It allows moderation for a list of conduct including that which is "otherwise objectionable, whether or not such material is constitutionally protected[.]" Who are you to say they don't find certain content objectionable?
I would hold that Twitter, insofar as it censors political viewpoints at the behest of political parties (and in some cases, foreign sovereigns), acts as an “information content provider” to whom the provision you mentioned does not apply. I would hold this for several reasons:
(a) Twitter’s conduct contravenes the expressly stated purposes of the statute. In fact, it frustrates those purposes.
(b) Twitter actively promotes opposing political content that is “objectionable” for the same reasons (according to the TOS), showing that their objection is not genuine.
(c) Twitter is acting against a broad class of persons, encompassing roughly half the country. The sheer numbers warrant exacting scrutiny.
(d) Twitter’s actions could affect our elections (and indeed appear tailored to that objective), and thus implicate interests beyond “constitutionally protected” speech. In that capacity, Twitter purports to flex not just statutory rights, but political power. To that end, it affects the sovereign interests of the USA, and the integrity of our processes.
(e) Twitter’s behavior is oppressive. They’re a gigantic corporation, and they’re censoring political speech of natural people, for no reason other than the fact that they disagree.
(f) To the extent section 230 burdens “constitutionally protected” First Amendment rights of natural persons for the benefit of corporate citizens, it is unconstitutional. As the EO says, the internet is the new public square, and we have a right to speak, regardless if Twitter arbitrarily deems our speech “objectionable.” Because, as a corporation, Twitter’s speech is fundamentally commercial, it is afforded less protection under the First Amendment, and it must yield to our superior First Amendment interests.
I can respect a difference of opinion. But tell me... do you not find Twitter’s conduct reprehensible? And if § 230 protects that conduct, why would you want it to persist? If Twitter wants to hold that kind of power, they need to at least win an election. It cannot be acquired by way of gift from the legislature.