Earth to you. That only covers Government vs people and sometimes employees and landlords.
A private business can refuse to serve you for any reason, or for no reason, as it sees fit.
I have outright refused to train a few people that I am uncomfortable with. - Or that I just don’t like the look of, for that matter. And I made no bones about it, either.
I am a flight instructor. - And this lawsuit involves my tagline.
Unfortunately you are completely wrong. It's a nice thought, and you would expect as much in a free country, but you are wrong.
Think about it this way. Can a restaurant refuse to serve blacks?
That’s how it should be, per the Constitution, but it’s not current law for any public accommodation or conveyance. And in many states, even your private flight instruction activities would be subject to broad anti-discrimination laws.