Such a proposal would seem to be illegal, according to the U.S. Office of Special Counsel:
Generally stated, § 2302(b) provides that a federal employee who has authority over personnel decisions may not:
(1) discriminate against an employee or applicant based on race, color, religion, sex, national origin, age, handicapping condition, marital status, or political affiliation;
Of course, Gingrich has already indicated that, as president, he’d feel free to ignore Supreme Court decisions. Why, then, would he feel restrained by the Office of Special Counsel?