Note, however, that the “erotic materials” statutes exclude public libraries from prosecution:
Exceptions to RCW 9.68.050 through 9.68.120. (RCW 9.68.100)
Nothing in RCW 9.68.050 through 9.68.120 shall apply to the circulation of any such material by any recognized historical society or museum, the state law library, any county law library, the state library, the public library, any library of any college or university, or to any archive or library under the supervision and control of the state, county, municipality, or other political subdivision.
That leaves the question of how someone would challenge material in a library. Generally, they first would take the matter to the library board. After that there would be a challenge in county superior court. However, since banning books raises First Amendment issues, it is possible that the challenging party could attempt to bring in action in federal district court. Both state and federal courts may have jurisdiction.
From my review of cases, most of the challenges to books are for school libraries. The big topic now for public libraries is internet access to allegedly-obscene materials.