This is not a valid comparison.
The question is not whether they have the right to discriminate (both do) but whether the discrimination is such a terrible thing. Racial segregation is much worse than gender separation. In fact, women are allowed to play at Augusta if they're invited by a member, just not to be members of the club. If Augusta did not want to allow blacks to become members, FReepers would be up in arms about it. Whether they have a right to do something like be a whites-only club is not the same as whether they are morally right. If the kids wanted to hold single-gender proms (a guys' prom and a girls' prom) FReepers would not blink an eyeball.
Discrimination on the basis of race and discrimination on the basis of gender are two very different things. Don't try to equate them, because it just doesn't work.