The Keller Independent School District, just outside of Dallas, passed a new rule in November: It banned books from its libraries that include the concept of gender fluidity. The change was pushed by three new school board members, elected in May with support from Patriot Mobile, a self-described Christian cellphone carrier. Through its political action committee, Patriot Mobile poured hundreds of thousands of dollars into Texas school board races to promote candidates with conservative views on race, gender and sexuality including on which books children can access at school. The issue has been supercharged by a rapidly growing and increasingly influential constellation of conservative groups. The groups have pursued their goals by becoming heavily involved in local and state politics, where Republican efforts have largely outmatched liberal organizations in many states for years. They have created political action committees, funded campaigns, endorsed candidates and packed school boards, helping to fuel a surge in challenges to individual books and to drive changes in the rules governing what books are available to children. The materials the groups object to are often described in policies and legislation as sensitive, inappropriate or pornographic. In practice, the books most frequently targeted for removal have been by or about Black or L.G.B.T.Q. people, according to the American Library Association.