Over the past year, critical race theory has gone from arcane legal concept to potent political rallying cry, as Republican legislatures have rushed to introduce bills banning it and other “divisive concepts” in public schools.

The furor over the subject has sown chaotic protests at local school board meetings, and is credited with contributing to last week’s election victory by the Republican Glenn Youngkin, who promised at nearly every campaign stop to ban critical race theory on his first day in office as Virginia’s governor.

To their proponents these bills represent a legitimate effort by parents to use the democratic process to shape education. But the measures have been widely assailed by Democrats (and a few conservatives) as a threat to liberal education and to the teaching of even some of the most basic facts about American history.

In a new report released Monday, the free expression group PEN America emphasizes what it says is another threat they pose: to the free speech guaranteed in the First Amendment.

“These bills appear designed to chill academic and educational discussions and impose government dictates on teaching and learning,” the report says. “In short: They are educational gag orders.”

“Taken together,” it continues, “the efforts amount to a sweeping crusade for content- and viewpoint-based state censorship.”

In invoking free speech, PEN is staking its approach on a principle that has lost its luster for some on the left, even while many on the right — including politicians advocating these bills — have invoked it as a mantra.

In an interview, Suzanne Nossel, PEN America’s executive director, said the intention wasn’t to endorse any particular curriculum or pedagogy, but to appeal to “higher principles” amid an increasingly polarized discussion.

“We’re not asking people to fall silent in terms of deliberation over how this racial reckoning is transpiring,” she said. “But the speed of the resort to censorship, without any apparent awareness of the contradictions, is part of the broader erosion of free speech in our society.”

The impetus behind these laws dates to last September, when President Donald J. Trump issued an executive order banning federal agencies and contractors from conducting diversity trainings that draw on “race or sex scapegoating” or promote “divisive concepts,” such as the claim that “the United States is fundamentally racist or sexist.”

That order was rescinded by the Biden administration. But the campaign against critical race theory — an analytical framework originally developed by legal scholars that has been adopted by conservative activists as a catchall term for various teachings about race — has only intensified as it has moved to state legislatures and local school boards.

Since January, according to PEN, legislatures in 24 states have introduced 54 separate bills aimed at restricting teaching and training in K-12 school, higher education and state agencies and institutions, by banning various “prohibited” or “divisive” concepts, mostly relating to race, racism, gender and American history.

Many are framed as protecting sound teaching, free of “indoctrination.” In June, for example, Florida’s state board of education passed new rules banning ‘critical race theory, which stated that instruction on required topics “must be factual and objective and may not suppress or distort significant historical events.”

“We need to be educating people, not trying to indoctrinate them with ideology,” Florida’s governor, Ron DeSantis, said before the vote.

Governments and school boards have wide leeway in setting curriculums in K-12 public schools, where courts have generally held that teachers do not have the same degree of academic freedom as those in universities. But many of these bills, PEN argues, are written so vaguely that they may chill a broad range of speech.

“This over-breadth and ambiguity is why they are so alarming,” Jonathan Friedman, PEN’s director of free of expression and education, said. “The truth is, most administrators and general counsels will quickly say, ‘let’s not run afoul of this.’”

Erwin Chemerinsky, a First Amendment expert and the dean of the law school at the University of California, Berkeley, who previewed the report, agreed. “Whenever the government regulates speech, it has to be clear about what’s prohibited and what’s allowed,” he said. “These laws are so vague in their wording that a teacher can’t tell.”

According to PEN, nine bills specifically target critical race theory. Eleven bills explicitly ban lessons based on the 1619 Project, an initiative by The New York Times Magazine exploring the history and continuing legacy of slavery that has been adapted into a classroom curriculum.

So far, by PEN’s count, 11 bills have become law, in nine states, sometimes within days of being introduced. Another 18 are pending from the 2021 legislative session, and six more have already been drafted for consideration for 2022.

Many of the bills, according to PEN, include language that purports to affirm freedom of speech and thought. Ten bills prohibit schools or teachers from “compelling” a person to affirm belief in a “divisive concept,” while eight mandate “balanced” teaching of “controversial” topics. (In Texas, such a law recently led one school official last month to suggest that educators who teach the Holocaust should make sure to have books that offer “opposing” views.)

Jonathan Zimmerman, a historian of education at the University of Pennsylvania who previewed an early draft of the PEN report, called it “the single best description and analysis of these laws.” And he pointed to the irony of conservatives who complain about “cancel culture” promoting such bills, which he called “the most profound and troubling example of cancel culture” today.

But he said liberals and progressives needed to wrestle with another irony. If you dig into the text of the laws, he said, they echo one of the arguments that have increasingly been used to justify limiting speech on college campuses — the idea that if speech upsets people, it should be forbidden.

“An idea that took root on the campus left is now being weaponized by the right,” he said.

Zimmerman also questioned the claim, common among critics of the laws, that critical race theory is an advanced concept that is not actually being taught in K-12 schools. Texts by legal scholars like Derrick Bell or Kimberlé Crenshaw may not be on the syllabus, he said. But some of its basic tenets — for example, that colorblind laws can strengthen structural racism — are broadly influential in many lessons and training materials, where they are sometimes stated as axiomatic truths.

“Some of the oxygen for these laws, as despicable as they are, comes from a suspicion there are people on left who do want to impose an orthodoxy,” Zimmerman said.

Last month, a group of educators and civil rights organizations filed suit against Oklahoma’s ban on critical race theory, on the grounds that it violates the First Amendment.

But the battle over critical race theory may be more political than legal.

In an interview, R.R. Reno, the editor of the conservative journal First Things, called the laws “a response to bureaucratic capture” of the education system by “radical voices” who do not represent the majority.

“Most voters will not be swayed by these nuances,” he said of PEN’s free speech arguments, which were summarized by a reporter. Some of the bills might be “terribly defective,” Reno continued. “But if that’s not the way to regain control of the educational establishment, tell us what the right way is?”

Nossel and Friedman of PEN said that the goal wasn’t to shut down public debate over how race and other contentious subjects are taught, but to ensure that debate can happen, including in the classroom itself.

“You can’t say you support free speech and say you support these bills,” Friedman said.

Nossel added: “Or even be silent about them.”