In the south many restaurants did not sell to African-Americans. Those restaurants did very well in the free market compared to restaurants that sold to African-Americans.
The market would have eventually driven these discriminatory businesses to bankruptcy. Majority public opinion had changed. That's why we were able to pass the laws. Would there be some holdouts? Maybe, but they probably wouldn't have lasted in the face of protests and pickets and lack of customers. Those that did would not be numerous enough to matter.
The landscape may have evolved since, especially with large companies, but if you don’t believe there are still scores of small businesses in small towns who get away with discrimination on a frequent basis, you should get out some more.
Capitalism actially straight up sometimes requires regulation. Sorry.
Money is power, and nothing concentrates wealth like capitalism.