The US Constitution created a massive firewall between Federal and State rights.
The US Constitution recognizes the right of a State to a jury trial in disputes of over $20. Not seeing any other "States' rights" in there. The Rights it lists are Rights of the People.
So they used interstate commerce to justify their intercession into State business. Reading the case and how food crossing state lines, as used at the BBQ in question seems like an egregious overstep of anti-Constitutional authority possible to justify forcing accommodation to all people (I can easily see purists in here arguing against that). From a bare technical legal look, it seems thread thin.
Why? Selling food from out-of-state looks like interstate commerce to me. Just like the Mann Act -- the feds wanted to outlaw prostitution so they said "transport any woman or girl across state lines for any immoral purpose". This was back in the day when the SCOTUS was still a court of law and hadn't evolved into the House of Lords it is today. Nowadays you get a Gonzales v Raich, where growing weed on your own land and smoking it yourself counts as interstate commerce to the SCOTUS.
That's thread thin. The Civil Rights Act? Not so much.
(Now I'm getting verklempt -- talk among yourselves. I'll give you a topic -- "interstate commerce" is neither interstate nor commerce; discuss.[/SNL])
I see this new Bizarro SCOTUS that aims to Plessy v Ferguson the nation back up, caring more for the technicalities of the law instead the heart of it.
I guess that depends on what you see as the heart of it. If you see the function of government to be holding down class enemies so you can impose your will on them, maybe so. But I'd have thought the heart of judicial review is to have limited government rather than a British-style unrestrained Parliament.
The justification for reversing Plessy v Ferguson is not that it was bad for the country but that it was wrongly decided. Go read
Bostock, the Gorsuch decision that upheld the rights of gay and trans people. If you think different rules for different people based on race technically qualifies as "equal protection of the law", you're reasoning like Alito, not like Gorsuch -- and not even Alito wants to Plessy v Ferguson the nation back up, though his explanation for why not was painfully strained special pleading. As for the majority, they sided with Gorsuch.