A false alarm on free speech
It is recognized by law and nature that minors are properly under the authority of their parents, not schools.
The big problem with David French's warning about free speech is he conflates things that are not the same. Regulations on curriculum for K-12 students are simply not the same as restrictions on what universities are allowed to teach or what private corporations are allowed to do. Restrictions on what adults are allowed to say to each other or what social media companies must allow on their platforms are largely irrelevant to discussions on what should be taught or discussed in classrooms in K-12 schools.
Primarily, this is because K-12 curriculum is almost exclusively taught to people who are under 18 years old. It is recognized by law and nature that minors are properly under the authority of their parents, not schools. As such, parents do have a voice in what their children are taught, especially on controversial social and sexual topics beyond the mechanics of human reproduction taught in a biology class.
When you are on the clock, you are expected to do your work in the way your employer instructed. Therefore, it is not a violation of a teacher's free speech rights when he or she cannot discuss details of his personal life in the classroom, even in a G-Rated way. If, as French proposes, students ask why someone has two parents of the same sex, the teacher can easily deflect and move back to the subject being taught. This is not the legal and professional minefield that critics are portraying.
As far as books being banned, there are some books that children should not be reading in schools. The most obvious is pornographic content - anything depicting sex acts. The act of taking certain books out of school libraries should not be controversial, and no one is preventing the local public library from carrying them. No one is removing those books from various reading apps for smartphones and tablets. Obviously, it is dependent on what books are being removed and why, so simply sounding an alarm about books being "banned" misses important context and nuance.
Critical race theory is a thornier issue. Now, let's be perfectly clear: It has been well documented that certain aspects of CRT are being taught in K-12 schools. Once again, that is where the schools' education mandate runs up against parental authority. But as French points out, teaching about our nation's troubling past on race is not the same as teaching CRT. We should teach about history, but that history should not become propaganda about the country being terrible today because of things that were done in the 1850's or the 1930's. Unfortunately, because this issue is so politically charged, where to draw that line is going to be unclear. But once again, what to teach minors who are properly under their parents' authority is not the same thing as regulating speech between adults.
Is the populist Right slipping away from the protections of free speech that have been traditionally embraced on the more libertarian right? Perhaps, but debates about what is taught in K-12 schools is not the right place to determine the answer to that question. Teachers do not have the "right" to share their opinions on divisive issues in a K-12 classroom. They can do that on their own time.