The first two women were admitted as members of Augusta National Golf Club. The exclusion of women up to now has been compared to the exclusion of certain races in the past. Is that a fair comparison? Not exactly. The difference between a man and a woman is different than the difference between a black person and a white person.
One similarity is that in both cases the historical disadvantaged group can exclude the historical oppressor, but not the other way around. A "Whites Only" club is horrible. A "Blacks Only" club is fine. A "Men Only" golf club is sexist. A "Women Only" golf club is feminist. There is validity to this point, particularly so long as the wealth and power of the country and of the world is concentrated in the hands of white men. What is the endgame though? Are we hoping for the day come when a men's club is again acceptable or when a women's club is equally unacceptable?
God supports sexism but not racism. There are some rather racist parts of the Old Testament, in favor of the chosen people, but anyone could, in theory, join the chosen people. The policies were against mingling with those who did not join, the uncircumcised. Sexism, however, is fully supported throughout. The male only priesthood and other very specific gender roles are encoded in the Law. Jesus treated women with great respect, but treated them differently than men, not least by failing to choose a single woman to be one of the Twelve, though this would have been completely acceptable in the culture: a woman Apostle sent to preach to the women. And then St. Paul has so many sexist lines.
Orthodox Christian theology requires believing that men and women are not the same. They have the same human nature, but the difference in the body means a different role in Christian society. If this distinction is completely wiped out, many doctrines no longer make sense, above all the male priesthood and the masculine language for God. But does this proper sexism carry through to civil society? Are we better off when it is restricted to the religious sphere or when it is reflected in the political sphere?
Of course the ideal is a civil society that perfectly reflects religious truth, but we are not working with the ideal. In the world as it actually is, we are often better off with a civil society that is empty of meaning, where we are free to be in the Church. When civil society claims that it is reflecting Christian values, it is often doing so for the wrong reason. Did Augusta exclude women because it wanted to be a place where men could cultivate the virtues of masculinity and a feminine presence would per se prevent this? Probably not. It probably started because of a lack of respect for women and because men wanted to sin in a certain fashion without women around, or rather only with women around who were in a subservient role. It probably continued for these reasons and also a false devotion to "tradition".
So it is no loss to society to have an integrated golf club, but it will be when other organizations are not allowed to be sexist. My Catholic university would not allow the formation of the Knights of Columbus because all student organizations had to be gender-neutral in membership. Masculinity is not an evil. Machismo is. Society is better off if there is a place for men to go learn how to be men, which is best done without women around.