A gender-based classification is subject to equal protection challenges. This isn't an issue of semantics, no matter how much you insist it is. "Dog" and "cat" aren't protected classifications under the equal protection clause. Certain characteristics of humans are protected from unequal treatment, and gender is one such classification. Defining marriage at the government level as between one man and one woman is a gender-based distinction. How you, Ontologuy, personally want to perceive the word is irrelevant to the discussion. The legal distinctions are the subject.
Your ignorance of the mechanics of equal protection is something you should really address before making the sort of statements you make.
Your projected ignorance of the matter is simply that.
Calling something a "gender-based" issue does not in any way make the issue subject to the equal protection clause.
The issue itself must be truly gender-based. This issue is not gender based.
Both the male and female genders have every right to be married, thus there is no gender discrimination in the matter.
That marriage is between a man and a woman as husband and wife is constitutionally acceptable, allowing both genders to participate, without bias.
Your erroneous application of gender-based would allow a woman to enter the men's locker room, strip, and take a show with the men, against gym rules .. or vice versa. For the sake of social propriety, there is nothing in the constitution that forbids the gym from creating these rules, banning any member who violates them.
If a woman/man who enters the opposite gender shower finds another of the opposite sex there who doesn't mind, or in fact encourages it, in no way constitutes a valid constitutional appeal to the gym's rule; just because a relative few are okay with the violation does in no way validate the violation, much less make the matter a "gender-based" issue.
That you lament my accurate dog/cat analogy is because again, it is an accurate commonly understood presentation that illustrates the oxymoronic "gay-marriage" violation of both definitive and social propriety, which, of course, flies in the face of your erroneous take on the matter.
Your concern of understanding "equal protection" is not at issue here.
What's at issue here is grasping when application of "equal protection" is not appropriate .. or, in your case, contrived for the sake of ideological gain at the expense of both definitive and social propriety.
Your attempt to apply the equal protection clause via appeal to "gender based" is rightly rejected.