Not quite.
The First Amendment is a restriction on the government's a ability to restrict speech. Virtually all the Bill of Rights and most other constitutional Amendments are restrictions on government (specifically the federal government (with the 14th being one of the few that specifically targets States).
For instance, if you say something I hate is my house, I can tell you to not speak or throw you out if you don't. I don't violate any of your constitution rights by doing that.
It's how the Augusta can get away with refusing membership to women and not violate the 14th Amendment. There is no state action involved.
What grates my nerves the most about those who booed and those who stand behind Perez is that its blatantly selective. They can support such behavior because they agree with what he says, but if the positions were reversed and it were they're views under assault like that, they'd be marching in the streets demanding that the judge be reprimanded and the crown given to her.
It's amazing how easy it is to accept or support such a thing when it's not your views that are being targeted.
Winning Ms. America should not be contingent on the contestants sharing the views off the judges.