You may want to read the 14th Amendment.
Especially the part where it applies to behaviors.
The 14th Amendment was never intended to cover making all behavior equal though. Or making all beliefs equal either. Especially some sort of sexual belief system.
If the 14th Amendment was used to force people to accept certain behavior and thus deny them a right to have representation on how that behavior or belief was dealt with in public then it would be denying EQUAL rights to representation for ALL.
So in other words that left-wing interpretation of the 14th Amendment would be FORCING a minorities political and moral views on the majority and would be being used to deny equal rights for ALL.
Just because you can identify yourself by your behavior does not mean that your behavior deserves to have the government force everyone else to accept it.