From what I read regarding "The Alternative Factor" NBC had two reservations. Yes, they were uneasy about the depiction of an interracial romance, but they also were bothered by the idea of Charlene Masters betraying Kirk and the ship to help Lazarus. They felt that Masters betraying her commanding officer and her oath and responsibilities would seem too much like Marl McGivers' betrayal in "Space Seed," particularly since the previous episode happened not long earlier and in the same season. I didn't get the sense they outright forbade the romance and the betrayal element, but they didn't care for either.
It follows that if you eliminate the romance then you have no grounds for establishing a betrayal. They tried writing it so that Masters could help Lazarus without betraying Kirk, but it doesn't seem to have worked well enough to anyone's satisfaction. The final alternative was to recast the role of Masters with a white actress, but they didn't really want to do that either. So in the end they kept the actress and her character but just eliminated the romance and betrayal. Thus Masters became just another crew person that served no real dramatic function.
I didn't get the sense that anyone really fought over this, but that it was just one more thing that was going wrong and most everyone just wanted to get this one over with and be done with it.
I always wondered why it had to be Kirk alone that had to force Lazurus into his ship when he had Spock and a security detail right there to help him out.