In the United States, as some related answers point out (like this and this), Section 230 (47 U.S.C. § 230) protects online forum providers from both civil and criminal liability for user content they host.
Consider this scenario: a user posts some content which is seen really horribly illegal or objectionable by many, and for which the user would quite likely go behind the bars. The forum admin receives a number of complaints but takes no action. Their position is "We are impartial. We value free speech and we are not the ones to judge if this content is illegal and apply censorship. If a court decides the content needs to be removed, we'll comply".
(Let's take copyright/DCMA out of the equation — there's separate clear removal procedure).
Is it really so that the forum admin will not be held liable?
Issuing a court order to remove the content may take a while, during which it will remain online (the user who posted it wouldn't remove it) — does that not to any extent weaken the admin's Section 230 protection? To elaborate further, the content may actually start causing apparent harm like, for example, someone who reads it starts committing violence, social/racial disharmony is caused and so on.
If the admin will be held liable, how exactly would that work around Section 230?
P.S. I know that in many countries they will be held liable. This question is specifically about the United States.