Sorry to butt in, but it seems like you're conceding an incorrect premise by
@Cubo de Sangre, that the offering of goods and service advertised to commerce (interstate or otherwise) is itself an alienable unit of speech that the government has the right to abridge. Since the CRA was passed, commercial speech and advocacy through commercial proceeds has gotten a bit more muscular in First Amendment analyses, but there is still no real precedent that the goods/services themselves are protectable speech. And it hadn't even been considered whatsoever in 1964. Commercial speech wasn't even a real thing until ten years after the CRA was passed.
Your white socks and mayonnaise store can still to this day spend money saying discrimination should be legal. They can erect billboards saying "we have tasty schnitzel and n****** are ruining our country." That's protected commercial speech that also happens to contain protected political speech. The CRA did not and does not curb that ability. You can still participate in international commerce while making really awful and discriminatory speech. You just can't withhold goods and services along the lines of protected classes. The fact that the production of goods and services offered to the public are not themselves speech is kind of implied in the context of compelled corporate speech in the area of required disclosures ("this is flammable," "smoking can cause cancer," etc.).
That's why the gay cake case was relevant: because the good/service involved contained political speech within it, or as least that's what the plaintiff argued, and that political speech was inconsistent with religious beliefs. It is at least arguable that making a cake that says "gay sex is groovy" is declaration of political speech. Offering public accommodations to black patrons really isn't. And you're still free to say they suck.
A little light reading:
https://www.scotusblog.com/2018/06/symposium-the-first-amendment-protects-speech-and-religion-not-discrimination-in-public-spaces/#:~:text=Contact Us-,Symposium: The First Amendment protects speech and religion,not discrimination in public spaces&text=The Civil Rights Act of 1964 transformed segregation in the,Supreme Court case – Newman v.
