> Why would this be a better example
Because it doesn't specifically deal with members of a protected class, and follow-on discussion about which classes should have protection, nor real-world issues like how private clubs and religious organizations can legally discriminate against those protected classes, or how theater and movie productions can require an actor to be of a certain race (a Bona Fide Occupational Qualification).
> the government can limit the ability of any business to refuse service
It's very well understood that the government has that ability. The government can also force a business to allow someone in who is (or is not) not wearing an N95 mask, and also force a business to allow someone in who is exercising open carry.
There are many such examples.
Given that, why single out civil rights law and its associated sets of who may be discriminated against (discrimination against Jets fans is usually not illegal) and explicitly allowing discrimination, along with a dedicated federal agency (the EEOC) to interpret and enforce the law, along with equivalents at the state level?
Is it because you think your proposed changes requires that level of enforcement bureaucracy, and can't be handled by the current criminal or civil code?
> For certain definitions of 'follow'.
The legal definition is all that matters. Give a relevant counter-example.
> I'm suggesting a change in the law which expands the reasoning that such decision might be deemed to not be totally legit
And I pointed you to a Supreme Court interpretation which says that law will be found unconstitutional. United States v. Colgate & Co., 250 U.S. 300 (1919). https://supreme.justia.com/cases/federal/us/250/300/
Your law, should it somehow pass, would be knocked down by the courts. You need a constitutional amendment to justify this level of restraint of free trade.
Civil rights law says that restraint of free trade is possible because there is a tension between the exercise of free trade and the Equal Protection Clause of the 14th amendment, and Congress has the power to find that balance.
Requiring customers to open carry, or to wear (or not wear) a mask are also based in interpretations of constitutionally allowed powers.
Your proposal does not give any similar justification for restraining free trade.