This is where the language causes me to differ. You have a right to GET healthcare - a doctor or hospital should not refuse to help you because of your race or religion and so forth.
Call it "right to access". A college should not be allowed to refuse a student because of their race - ACCESS - but they should not be required to provide it for free. Or even cheap.
Ditto a store - a taxi - a restaurant - and so on.
As an example, we regard driving as a "privilege". You don't just drive on the roads. We accept that.
Years ago, when we rode around on horse-drawn carts or rode on horses, there was no such thing as a carriage or horse license and you didn't buy horse insurance.
The roads were still there, but anyone had the right to use them. We regard it differently now.
People are using the word "right" interchangeably with "access". You can buy a house - no one may prevent you. But the state is under no obligation to provide one.
You may start a business and you can get a bank loan - if you can qualify - without regard for your race or religion. But they don't hand out businesses and loans for free.
I like these discussions. I do, respectfully, disagree with the semantics.
While I view hospitals and restaurants differently, in general I would say any private commercial enterprise should be allowed to discriminate based on race or religion or so forth. That's stupid of them to do, but in my view it is their right. Since hospitals receive federal funding for many patients, and are closely regulated because of that, and they provide life and limb services, they should not be able to discriminate on factors such as that.
I think we are saying the same thing, though, with respect to access. As in, I have the right to receive (have access to) healthcare, or restaurants, or Walmart, or wherever, but that does not mean that someone MUST therefore provide healthcare, or insurance, or Italian food, or cheap Chinese products to me. They have the right to do so or not (with the aforementioned life-and-limb caveat). This is to say I have the right to keep and bear arms, but that does not mean that Winchester must make them, nor that the government must provide one to me. I have the right to receive healthcare, but no one is required to be a doctor or nurse, no insurance company must provide me insurance to help pay for my healthcare, and the federal government is not mandated to provide me with in health care nor insurance to make it cheaper to get.
Anyone and everyone has the right to drive on the roadways, but - for public safety - STATES (not the federal government) have standards for who is allowed to travel. You must prove you are safe to do so. No one just gives licenses (unless, of course, you know a guy), but you cannot be stopped for any reason that is not safety related.