The objection is one of discrimination, and how discrimination is wrong no matter who it is applied to. Your "feelings" aside, this is the logical position to take. In fact what the Alamo Drafthouse did was against the law, because as a merchant selling to the general pubic you cannot discriminate on the basis of sex. The only writing I have seen complaining about this fact is from Liberals who seem to believe EVEN MORE discrimination can - somehow, in some magical way, "make up" for past wrongs.
This is not because I say so - logic bears this out. If Alamo Drafthouse would advertise a "white only" showing, you would be just as pissed but for diametrically opposing reasons. In other words, under different circumstances - that you happen to "feel" are right - you would be adopting the Conservative position. Merely because you LIKE discrimination does not make it right.
To coin a phrase, if the logic fits you must acquit.