This equal rights principle is implied by "all men are created equal" and both parties would support the explicit amendment, maybe for different reasons. The red camp wants to end "affirmative" action, while the blue camp wants to affirm rights of minorities. I guess the wording of the amendement is what would cause a fight.
Scalia disagreed. He says only purpose of the 14th amendment was to make sure slaves were on equal footing. If women had rights they wouldn't have needed an amendment to vote.
He's dead but at least five people almost certainly agree with him.