Fairness in Higher Education Accreditation Act This bill establishes additional requirements for an accrediting agency to be recognized by the Department of Education as a reliable authority on the quality of education being offered at an institution of higher education (IHE). Specifically, the bill prohibits an accrediting agency from considering (1) the diversity, equity, and inclusion policies of an IHE; and (2) the racial composition of the accepted applicants, students, or the faculty or staff of an IHE. An IHE that is subject to a denial, withdrawal, or termination of accreditation as a result of an accrediting agency's violation of this prohibition may pursue a civil action. The bill also requires an accrediting agency to assess the IHE's success in ensuring a right of free inquiry (with an exception for religious IHEs). In the case of a public IHE that is legally required to abide by the First Amendment, the bill defines free inquiry as compliance with (1) the First Amendment, including protections for freedom of speech, association, press, religion, assembly, and petition; and (2) the IHE's own written policies regarding academic freedom. In the case of a private IHE, free inquiry refers to adherence to the IHE's written institutional policies concerning freedom of speech, association, press, religion, assembly, petition, and academic freedom.