The planned eliminations are in response to a new state law ordering public colleges to cut certain academic offerings and invest in high-demand fields.
The Foundation for Individual Rights and Expression, which is representing the plaintiffs, said targeting learners based on speech violates their rights.
Together, the orders set up the administration to exert more control over who institutions enroll and which grants are funded.
In his announcement, Florida Gov. Ron DeSantis slammed the current system as an "accreditation cartel" and decried diversity standards at accreditors.