That's your take, and mine is that owning a business doesn't entitle you to engage in racist business practices.

Your take is wrong. Once you make racist behavior illegal, you've given regulatory power of an unspecified scope to whoever controls the official definition of racism. This is the point I made in my earlier response which you conveniently ducked because you have no answer for it.

Kicking someone out because you don't like their hair can't be equated to not serving them because of race.

Sure it can. I just did it.

Let's look at this differently; if they were an employee at your business and you fired them for their hair, you could argue that it's unprofessional or unsanitary

I'm not arguing that. I'm arguing that I don't like their hair, and I don't want someone with that kind of hair in my place of business.

but to fire them based on race or religion hasn't got a justification of which I can think.

It doesn't need one. I own my business, I can do what I like with it. No one is harmed by the lack of access to my business.

Why should you be able to he sued for wrongful termination by the employee in the second example

I shouldn't.

a government which claims all men are created equal?

All men are created equal. No one on the face of this earth has a right to my services.

I'm not arguing a right to be served,

That's exactly what you're arguing, you just don't want to admit it because it's baseless and absurd.

I'm arguing a right to be treated as a person,

Being a person does not give you the right to be served in my business. Ergo, denying you service is still treating you like a person. How many times am I going to have to go over this?

I'm advocating for historically disenfranchised groups to be treated with the same respect you'd show anyone else.

And I think they should, but I don't think it's the government's place to punish people who disagree with me about that.

If you're refusing to serve all people, that's your prerogative but once you discriminate based on the factors I've discussed then I believe the government should have a place in curbing that behaviour.

Yes, I know you do. You've made your authoritarian beliefs quite plain. What you haven't doing is provide any logical or objective basis for them, or make any indication that you care about individual liberties or the threat of government overreach.

If "producing the same result" is grounds for comparison then I could argue that my murdering someone with terminal illness is fair game because they'd die soon anyway.

You can argue that, but you'd be completely wrong, because in one situation they live their life out naturally and in the other you end their life artificially.

In this case, you are inserting yourself into a moral equation with another person who cannot control your actions and that person is the one who suffers. In my example, the person who gets thrown out of my store a) does not suffer, and b) was not forced into the situation, but went into my store of his own volition.

To reiterate; I'm not talking about the right to shop wherever you want,

That's exactly what you're talking about, you just aren't being honest about it.

I'm talking about the right to not be discriminated against.

No such right exists.

Saying that you don't want to serve them because you're discriminating against them is dehumanizing.

No it's not. There are plenty of people I don't want to serve, and they're all still human. You can repeat this stupid bullshit as much as you want, but it will never make sense so you should probably drop it.

You're treating them as less than they are by focusing on one aspect of their identity and taking action based on that.

No, you're treating them exactly as they are, and saying you don't like how they are and shouldn't be forced to do business with them if you don't want to.

A hate crime is in a category of its own to address this very thing.

Hate crimes are also a ridiculous construct and should be done away with on similar grounds.