Unfortunately (for the politically correct) there are significant differences between men and women.
Particularly in the voice department.
As a "tiefer Alt" or true contralto who is often called upon to fill in for tenor, I am very familiar with this issue.
Without getting into the tall weeds on the issues of breath, resonance, falsetto, and vocal cords, women do not sound like men!. This is particularly true with the male alto/soprano sound that is the Whiffenpoofs' specialty.
Just for example, I want you to take a minute to listen to this very accomplished male alto singing a work that was written for that voice part - Orlando Gibbons' "This is the record of John".
Listen and you will hear that this is definitely a man, with male voice qualities, and a woman singing it would be completely different. I have in fact sung it - but I would never record it. Here's a local version with a contralto singing the solo part - over at Emory. Listen to the timbre, the breath - aside from the fact that they had to drop it 2 whole steps from the original key -
The women (especially women who have runaway soprano vibrato) are going to stick out like sore thumbs. Moreover, the director will have to change all the settings, harmonies and keys to accommodate the female voice.
R.I.P. Whiffenpoofs - you had a good run.
My simplified take would be making an all female barbershop quartet. There are ones out there but they sound nothing like what one would expect of a form of music that most rarely listen to, if ever. I occasionally don’t mind listening to a good one but the womens ones I heard on the web don’t make me want to hear them again.