According to the bill, parents may take legal action against their child’s school district and be awarded damages if they believe any of its policies infringe on their “fundamental right to make decisions regarding the upbringing and control of their children.”
Anti-war advocacy was a foundation of the American left in the middle of the century. But any free speech arguments were incidental byproduct of blacklisting/censorship leftists faced when opposing US propaganda.
To quote Gore Vidal: "For the average American freedom of speech is simply the freedom to repeat what everyone else is saying and no more."