The article says that it would impact public schools and public charter schools. The charter schools receive funding from the state, so they can just deny funding unless they meet certain criteria, which they already do. And that criteria could include not giving access to certain books to children.
It's tough because most people don't have a choice to pick up and move if they don't like their school board. As a parent, schools are a very important issue to me as it strikes at the autonomy you have as a parent. Many would have an issue with teaching religion in schools, and others would have an issue teaching gender studies in school. The compromise would be to limit the scope of education to the non-objectionable: science, reading, writing, math and history.
Normally I would want that decided upon on the local level, but given the nature of school zoning and difficulty of moving, I wouldn't be opposed to setting guidelines on a state level.