The term “public business” is very misleading, to say the least. It’s a private business. I don’t believe “Congress shall make no law...” ever was intended to pertain to anything except the government. We’ll have to agree to disagree because you will never change my mind on this.
And that’s fine, but after the civil rights era, doing what this guy did is illegal. You can not refuse service to someone over race, creed, or color. That is the federal law, and has been since the 60’s.
He is not running a private club, he is running a business.