Yes, and section 230 explicitly states that moderation does not waive that immunity:
(2) Civil liability
No provider or user of an interactive computer service shall be held liable on account of—
(A) 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 [...]
You're aware that comments on NYT articles are also human-moderated, yes?