Never heard of desegregation, then?
Desegregation concerns GOVERNMENT facilities and I support that 100%. I do NOT support the government telling me who I may or may not provide services to as a private business.
You're a big COTUS guy, you tell me how you justify it.
Firstly, I believe COTUS, or any Law, is only legitimate so long as it is good (just and fair) and the People consent (on the whole; individual disagreement is somewhat more complicated and the social contract really is an involved discussion unto itself). For example, I do not believe the Constitutional ban on abolition or the fugitive slave laws were legitimate or that the government was legitimate or to be obeyed when it tried to enforce them.
Secondly, I believe that rights have limits. To be succinct, rights end when it comes to violating another's rights.
When it comes to desegregation, I believe the infringement/limitation of the rights of association and non-association of private business owners was a necessary evil as allowing the system of entrenched ans systematic exclusion, segregation, and discrimination to continue constituted the greater travesty. As a part of the effort to end segregation and the exploitation and abuse of an entire race of persons, it was something that had to be done. In the real world, there are oft no perfect answer. Sometimes, unfortunately, we the choice we'd like isn't an option and it is all we can do to choose the lesser evil to fight or prevent the greater travesty.