In the US, the civil rights movement (in many respects a good thing) staged sit-ins at lunch counters. Black people would sit in an establishment that did not want them as customers.
Now, whose rights do we care about? The black people weren't starving. They had choices in where they got they're food. But the lunch counter owner had saved up his money, purchased a restaurant, and tried to set rules for the business that he owned. He didn't have a lot of choices. The lunch-counter was his only business. He had that, or he had nothing. But he was told he had no rights. His property wasn't really his property. Nope. He had to serve anyone that walked in through the door and he couldn't turn people away. He didn't have that right. His property wasn't so much his property, it was a "public accomodation".
I disagree with that. Property Rights were traded so that black people could sit at lunch counters. Did the black people gain so much? Or did we all lose a lot by losing control over our personal property?
Now, a smart businessman will serve anyone who comes in through the door. But the issue isn't "Is discimination a smart business practice?" It isn't. It's a dumb business practice. The question is how much control should the government have over your home or your business?
I vote for less government control.
Much of the problem, of course, was that Southern states didn't just allow segregation, they required it. Plessy was about a Louisiana law that forbade private railroads from establishing integrated cars.
Many of the restaurant owners to whom you refer may have wanted for business or moral reasons to integrate, but Jim Crow prohibited it.
In many instances, it was not the business owner who objected to serving blacks. Quite often, it was local government ordinances that prohibited him from serving blacks or fear of reprisal by white customers or hoodlums for doing so.
His property was not "his property" in those cases either.
Woolworths was the classic example where most of the "Lunch Counter" sit-ins took place. It was a nationwide chain department stores, and across the country, North and South, blacks were welcomed to spend their money in their stores on clothing, housewares or anything they wanted to buy including at the lunch counter in most of the country. Only in some areas did Woolworths refuse to serve blacks at lunch counters and only because of local laws or pressures from the community. It was not something that the "owners" chose to do. They were forced to discriminate in those stores.