I'm sure some NCAA official had the idea sometime that "If the women's championship is not the same weekend as the men's, we wold have a better TV contract. Attendance might be better too."
There's a reason why the women's basketball championship finals and the Frozen Four are the same weekend as the Men's. It's because CBS, which pay's a ton of money, wants it that way. Why does it? Wouldn't the games have more viewers (and the network could charge more for adds) if at least one event was moved to the following weekend? Yes, but it might interfere with the viewership of THE MASTERS!
For it's THE MASTERS ("like no other") that is at the heart of CBS Sports and everything it does. So they pay a little extra for men's basketball to eliminate competition.
Can I point to a smoking gun on this? No, but consider this: Twenty years ago, men's basketball games started on Thanksgiving weekend, a logical tine, since it was also the end of the football season (We always played at USC on Thanksgiving weekend because the Pac 10 season was over by then. Why, when the NCAA decided to extend the basketball season, would it choose to move into a football season (it's biggest moneymaker) rather than start the championship tournament 2 weeks later?
Back to your original point, as far as I know, nobody referees both Division I men and women's basketball during the regular season. Perhaps there's a rule against it. Perhaps the money isn't good enough, although I think the ACC would pay as much for women's referees as the Big South does for the men's games. I wouldn't want them to start doing women's games during the tournament.
There is no referee union. They are independent contractors. There's a separate board for those assumptions.