Legally, it should be added... The freedom protected in the first amendment is the freedom of political assembly. The Civil Rights Act has been argued repeatedly in the Supreme Court, and the court has ruled repeatedly that the constitutionally protected freedom of assembly is not curtailed by requiring corporations, incorporated under the rules of the state, to be required to serve everyone in the protected classes.
The court was wrong and will be wrong again.
I would ask how progressives square two contradictory interpretations of the first amendment but then I realized they don’t really support the freedom of non-progressive speech anymore.
(IANAL disclaimer) The freedom of association has been implied by analogy to be protected by the explicitly-enumerated freedom to peaceably assemble in the First Amendment, in some specific cases. But it's a loose protection by analogy; the letter of the First Amendment doesn't even mention a freedom of association. The SCOTUS has not ruled that the freedom of association extends to a freedom to exclude in public accommodation; in layman's terms, the reasoning is "You have the freedom to serve as many people as you want, but that does not imply a freedom to not serve other people if you want to operate under the corporate charter that the government grants."
This overview describes things much better than I can. https://constitution.findlaw.com/amendment1/first-amendment-...
> The court was wrong and will be wrong again.
No doubt, but I don't think you'll find a receptive ear (in the public or in legal circles) to the notion that the Court has been wrong regarding upholding the Civil Rights Act.