Yes. Segregation was both a private practice and a state enforced practice. What people fail to realize is that business were required to provide separate facilities. This does not mean that every business would not segregate without state coercion. But it did mean the law required them to. The problem is it swung the other way. The state shouldn’t have required people to segregate, but neither should it force people to integrate. Neither approach respects free association or private property.
I think it is an important point to clarify that it was the government that was behind the segregation. It certainly did reflect the social mores of the times, but it was the force of law that created segregation into the institution that it became, and not businesses.
If you look at the role that businesses play, the tendency is to go with the bottom line. If that means importing Chinese from the starvation of China at rock bottom wages, that is what businesses do, until the people protest and governments pass laws against further immigrants.
It is the bottom line that has made the Americas into the mixing bowls that they are today.
The thing about people at the individual level is that they integrate all on their own. Even if it is socially unacceptable to mix at one level, people in low places do mix, or the high and the mighty go slumming, and the end result is that integration happens and people have to deal with it. What government law does it to put up barriers,and set precedents that can be interpreted in a thousand and one different ways, and the law of unintended consequences kicks into effect.
The market and individual choice on a mass level has a way of sorting things out. Unfortunately, it is not the way of big government to trust in freedoms, and the laws that end up being made, either for segregation, or for integration, inevitably end up stifling the wisdom of the collective choices of individuals, who alone know best where their own interests lie.