I agree - IF we can also agree that groups for "White Women", "Bald Hispanic Men Under 40", etc... are also allowed.
Society needs to come to a consensus on this. Either there is a useful purpose to segmenting private groups by age, gender, race, income, etc... or there isn't. If there is a valid purpose, then we should all agree that all possible combination of these factors are equally valid.
The end result is that some poor white woman won't be able to attend because of the color of her skin. I'm not sure what happens to her mulatto friend...I guess it depends how black she looks.