Nope, that's not the argument here. The argument is whether the Texas sodomy law is "unconstitutional" because it allows punishes certain people for one kind of behavior, while letting other people engaging in the exact same kind of behavior get away scot-free.
If homosexuality is not a sexual gender, then where does the equal protection come from? Is it a race?
It is neither a "gender" nor a "race". It is a behavior that is usually ascribed to persons who are of the mindset to practice it. Not unlike "receiving Holy Communion" is a behavior ascribed to persons who are of the mindset to practice it, namely Roman Catholics.
If you are looking for a close equivalent to a class that is already protected by "equal protection", it would come closest to religion. They are both mindsets/sets of beliefs with specific practices related to those beliefs. To boot, both are "changeable" and are not fixed beliefs/behaviors.
They are "similar" behaviors but not the same behavior. Men interconnecting with women fit differenly than 2 men connecting or 2 women. The law is scoped that only one of these 3 pairings is acceptable (and that is the pairing that includes both a man and woman).
If the law only permitted 2 men to commit sodomy you'd be able to make your case since there would be no option for women to participate in sodomy (with another woman or a man).
Science (and the legal definition) prohibits members of the same sex from engaging in sexual intercourse ("Sexual intercourse" means any penetration of the female sex organ by the male sex organ.). Is that somehow unconstitutional too? Better team up with that guy from The Life Of Brian who wanted to give birth to babies, he declared that it was his right as a man.
If you are looking for a close equivalent to a class that is already protected by "equal protection", it would come closest to religion.
So much for the claims among the homosexual agenda crowd that it is "genetic". You put it under a belief system.
Some gourmands might claim that their faith in fine dining is being infringed on by preventing them from eating horse (and they could hold up all sorts of genetic data to show how close a horse is to a cow or deer).
Doesn't make it a relgion though (even Scientology existed for decades before President Clinton's administration officially recognized it).