You are espousing a libertarian argument against anti-discrimination laws.  This view may not be racist, but it is certainly uninformed about the social realities of Jim Crow. 

Racial segregation and discrimination by private businesses in the South was not simply the result of business owners' personal choices, but of pervasive societal pressure and coercion by local and state governments.  It's legality allows it to persist.

I appreciate your optimistic view, but the social rejection of racism was in large part driven by the legal banning of segregation.  Without such laws to jump-start the process, racism would have (at the very least) taken a very long time to die.