No grounds are needed. An employer can fire anyone, for just about any reason, unless that person is a member of a protected class. Several civil rights laws — starting with the granddaddy Civil Right Act of 1964 — protect people from discrimination on the grounds of race, sex, ethnic origin, pregnancy status, age, etc. Since 2020’s Supreme Court ruling in Clayton, sex now unequivocally also means sexual orientation and gender identity.
But no civil rights laws protect women who have sex outside of marriage. So a man like Ramsey is theoretically free to fire women for having sex.
A caveat applies. The woman admin assistant he fired for having sex outside of marriage is arguing in legal briefs that he fired her under circumstances that would not have got a man in his firm fired. If she can convince a jury of that, then she could prevail based on simple sex discrimination.