The law, passed during this year's legislative session, restricts the way certain race-related concepts can be taught in public schools and in workplace training.

The lawsuit, filed Wednesday in federal court in Tallahassee by two businesses and a consultant who conducts workplace training, alleges that the law is "an immediate infringement of plaintiffs' free speech rights."

"This law enacts unconstitutional viewpoint-based restrictions on the speech of Florida's business owners and employers operating within the state in violation of their First Amendment rights," the lawsuit said. "It employs nebulous terms with vague definitions to chill protected speech with which Florida's governor and certain elected officials disagree, while protecting speech more aligned with their viewpoints on certain issues."

The challenge was filed a day after Chief U.S. District Judge Mark Walker heard arguments about whether he should issue a preliminary injunction against the law, which is slated to take effect July 1. Those arguments came in a case filed in April by public-school teachers, a University of Central Florida associate professor, a child who will be a public-school student in the coming year and the president of a firm that provides workplace training.

As of late Wednesday afternoon, Walker had not ruled on the request for a preliminary injunction, according to an online docket. But during Tuesday's hearing, he expressed concerns about the plaintiffs' legal standing to pursue blocking the law.

DeSantis this year made a priority of passing the law — which he dubbed the "Stop Wrongs Against our Kids and Employees Act," or Stop WOKE Act. It came after the State Board of Education last year passed regulations that included banning the use of critical race theory, which is based on the premise that racism is embedded in American society and institutions.

The law lists concepts that would constitute discrimination if they show up in classroom instruction or workplace training.

For example, it would make it illegal to compel people in workplace training to believe that an "individual, by virtue of his or her race, color, sex, or national origin, bears personal responsibility for and must feel guilt, anguish, or other forms of psychological distress because of actions, in which the individual played no part, committed in the past by other members of the same race, color, sex, or national origin."

The new lawsuit was filed by Honeyfund.com, Inc., a Clearwater-based technology company that provides wedding registries; Whitespace Consulting, LLC, which does business as Collective Concepts and provides training to corporate clients; and Chevara Orrin, a Broward County resident who founded Whitespace Consulting and is described as an "expert on diversity, equity, inclusion and justice." The case names as defendants DeSantis, Attorney General Ashley Moody and members of the Florida Commission on Human Relations, which can investigate complaints about discriminatory practices.

The lawsuit, filed by attorneys from the national group Protect Democracy and the global law firm Ropes & Gray, alleges the law violates constitutional speech and due-process rights. It seeks an injunction.

The lawsuit said the plaintiffs believe it is important that training and other activities address issues such as diversity and structural racism in workplaces. It said, for example, it is unclear how Honeyfund can move forward with training scheduled later this year that would be consistent with the new law.

"Without such DEI (diversity, equity and inclusion) trainings, plaintiff Honeyfund would risk losing substantial benefits to its businesses, including improving collaboration and productivity, attracting more diverse candidates, increasing employee engagement and connecting with diverse clientele," the lawsuit said. "Honeyfund is best positioned to know what practices are best for its business."