Quoting directly from the American Library Association:
As challenges grow more frequent, it's important for library staff and trustees to know what to do well in advance of experiencing one themselves. If your library receives a formal challenge, please contact your consultant.
Before you experience a materials challenge, the library should be prepared with the following items:
Collection Development Policy: Explains the who, what, and why of how the library maintains its collection - including the mission of the library and the purpose of its collection, the criteria for selection, how the library handles gifts and/or donations, the importance of weeding/deselection, and a materials reconsideration form for formal challenges.
Reconsideration Process: A written process reviewed by library staff that gives patrons the avenue to formally request that the library reconsider whether that item should be included in its collection.
Patron Behavior Policy: Many times, people making complaints just want to be heard. Library staff should listen and acknowledge the person's right to question library resources. If the patron becomes disruptive, then staff should be guided by the library's patron behavior policy.
Talking Points: Whether you're responding to a formal challenge or informal complaints, it's important that library staff and trustees be clear and consistent. These guiding principles from the American Library Association may help you with your messaging.
ALA Joint Statement Opposing Censorship (11.29.21)
Calm (Legally) Cool, and Collected: an Empire State Library Network webinar with Ask The Lawyer attorney Stephanie Cole Adams.