Part of the question might be "should business owners be forced to serve all their customers equally?". I suspect the question is moot and business owners themselves were likely against segregation to a solid majority. Having two entrances looks expensive as does having a decorative wall or different systems to deal with certain customers. Businessmen who choose not to serve customers will exist, but they will be rare. As strategies go, "let's not have customers!" is a loser.

Racist business owners would be common. Business owners who let that get in the way of making money would be much less so. Greed is a great equaliser.