Thank you for asking politely. I'll address your post now.
I think our differences arise in your misunderstanding of the difference between a right and a government granted privilege.
A racist store owner or a non racist store owner should both have the ability to determine the use of their OWN bodies and their OWN property. I consider that their equal right and somewhat axiomatic.
To use ANOTHER persons body or to determine the use of ANOTHER persons property requires the consent of the other person, if it doesn't then there can be no such thing as equality. If you don't understand that point, I can explain it to you later if you like.
How other people decide to use their OWN property or their OWN body may meet with our disapproval, but to take away a persons right of self determination is wrong isn't it ? If you say yes to my question, then we have no argument. If you say no, then you are at least in part supporting unequal rights, as you would be endorsing one party having the ability to force another party when the other party is in a neutral status. In that instance, the onus of defending the use of offensive force falls upon you. I can't think of any proper moral defenses for the use of offensive force, can you?
"Open to the public" is a phrase you toss around, but then you fail to understand the contradiction. It can only be "open to the public" if the owner voluntarily wishes it to be so or if another entity forcibly imposes that status on the owner. right?
In the case of the hypothetical racist store owner clearly his intention is NOT to be "open to the public". If he isn't trying to run ANOTHER persons body or ANOTHER persons property, how would you or I have any right to tell him what to do with his OWN body or property ? Where would that right come from?