This isn't a private school. What makes this so egregious is that it's a public school fully funded by the public purse. But to answer your question about private schools, all religious schools in the U.S. have the legal right to discriminate against LGBTQ teachers, counselors, social workers, and in some cases even "lunchroom ladies" and maintenance staff. Congress and the Supreme Court have seen fit to exempt private religious schools from Title IX and other laws that prohibit discrimination based on sexual orientation and gender identity. In at least one case, the Supreme Court even forced taxpayers to fund the discrimination, against the explicit wishes of the state government.