Is it OK to force the Boy Scouts to have gay scoutmasters?
The Boy Scouts are a private club and have a right to determine membership. They are not offering something for sale to the public, or determining that they can only offer a product or service to select members of the public, they are a club for private association.
So would it be OK under your philosophy for the train company to make Frederick Douglass ride in the baggage car rather than forcing the people in the whites only train cars to associated with him?