Florida Governor Ron DeSantis is being sued over his "STOP Woke ACT," over claims the law violates free speech and hinders "professors' ability to teach and students' ability to learn."

A professor and student group from the University of South Florida has filed a suit against DeSantis arguing the legislation the Republican signed in law in April (full name Stop the Wrongs to Our Kids and Employees Act) will "impermissibly chill" free expression and promote "unconstitutional censorship" in higher education.

The act prohibits the teachings of lessons or business practices such as diversity training sessions, which could make people feel "guilt, anguish, or other forms of psychological distress" because of historic wrongs due to their race, sex or national origin.

In August, a federal judge blocked a section of the law from being enforced which would restrict private companies carrying out diversity training over fears it would violate constitutional laws of freedom of speech.

Florida Gov. Ron DeSantis speaks at the Unite and Win Rally in support of Pennsylvania Republican gubernatorial candidate Doug Mastriano at the Wyndham Hotel on August 19, 2022 in Pittsburgh, Pennsylvania.Jeff Swensen/Getty Images

Announcing the new lawsuit against DeSantis, the Foundation for Individual Rights and Expression [FIRE], said the First Amendment doesn't allow Florida law to declare which concepts are "too challenging" for students and faculty members to discuss.

The group said the act also does not allow students and faculty members to "play devil's advocate" and discuss challenging ideas.

"Without the freedom to engage in vigorous and robust debate about important issues and contentious concepts, a college education is just an exercise in memorizing facts and repeating government-approved viewpoints," FIRE attorney Adam Steinbaugh said in a statement. "That's not freedom or education."

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FIRE also accused the legislation of being "stuffed to the gills with vague language" that leaves professors unsure what topics they will be allowed to discuss in their lessons.

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Plaintiff Adriana Novoa, a USF history professor who previously lived under a dictatorship in her native Argentina, said the government should not be allowed to determine what people think and talk about.

"I know indoctrination. I've seen indoctrination. And indoctrination isn't coming from my classroom—it's coming from a law intended to limit the freedom to think and express these thoughts, which is the foundation of good education," Novoa said.

The act, along with the controversial legislating dubbed the "don't say gay" act, was introduced by DeSantis as the governor looks to expand his influence and install conservative values into education as part of his battle against the "indoctrination" of children.

The governor even weighed into the normally non-partisan school board elections in August, publicly campaigning for a number of candidates who would support his "DeSantis Education Agenda."

DeSantis backed a total of 30 candidates running in school board races in Florida. Of these, 19 won their August 23 elections outright, with a further six advancing into runoffs and five losing their races.

DeSantis has been contacted for comment.