Rights of a minority should not be put up a popular vote.
Rights for any groups should not be put up a popular vote.
And the fundamental premise to your conclusion is false. Ergo your conclusion is false. Deviant sexual behaviors while in the minority are not "a minority" when it comes to the 14th. Otherwise compulsive theft & serial killing would be protected behaviors repugnant to the majority. After all, they would argue, "we are born this way"...
You go opening that legal pandora's box and you might as well declare anarchy as the ruling principle of this country.
I am not sure if you could possibly get any more dramatic. Theft and serial killing denies the right to life, liberty, and the pursuit of happiness. Consenting adults engaging in homosexual sex does none of those things.
No see that's the thing. Blind justice doesn't get dramatic. It just examines precedent upon "same or similar" and acts accordingly, without prejudice. That's the problem and why the SCOTUS has to be very keenly aware of how things can spiral out of control. When y'all were petitioning for butt sex to be legal in Texas, you were assuring the public then to "not get dramatic...this doesn't mean we'll be trying to get gay married...we just want what we do in our bedrooms to be decriminalized..." Fast forward a couple of years and now y'all are screaming bloody murder that your "civil rights to gay marry are being denied!!"
So we anticipate that your steamroller isn't going to just suddenly stop dead in its tracks. We anticipate that you will pave the way for not just your little clique of deviant sexual behaviors you've labelled "LGBT" [yet still fight amongst yourselves if it includes the amorphic "Q" or not], but that you will also pave the way, quite logically, using blind justice, for polygamy as well. It's a no-brainer. If gay marriage gets federal protection then there is no reason whatsoever that a law school flunkie couldn't take his polygamist clients straight back to the SCOTUS next year and make polygamy legally-protected as well.
And as it happens, there is a group of polygamists petitioning for just that thing and have openly said this is precisely what they will do before the ink ever dries presuming the gay cult gets their way. Their attorney is no law school flunkie either. He is Jonathan Turley and he is no slouch.