In general, under AP Style, use terms that can apply to any gender. Such language aims to treat people equally and is inclusive of people whose gender identity is not strictly male or female. Balance these aims with common sense, respect for the language, and an understanding that gender-neutral or gender-inclusive language is evolving and in some cases is challenging to achieve. Consider any word or term that has the effect of emphasizing one gender over another. Is there another word that could be substituted? For example: search instead of manhunt. Police officer instead of policeman. Door attendant instead of doorman.
A true gender-neutral noun often presents itself easily: chair, firefighter, workforce, first-year student. In other cases, a noun may technically not be gender-neutral but instead be a masculine noun that assumes the generic case under English language convention: actor, host.
In general, use terms such as chair or chairperson, councilperson or council member, and spokesperson unless the -man or -woman terms are specified by an organization. Councilmember is acceptable in jurisdictions that have adopted the one-word version.