This is illegal per the Civil Rights Act of 1964. The only way you can limit access is to make it a private (ie: members only) club.
The only way you can limit access is to make it a private (ie: members only) club.
First of let me say that a number of private clubs have been forcibly integrated by the courts. Gender and not race has been the main cause for such actions. But more importantly here, is the idea that private clubs is the "only way." Imagine if some one had said that due to the Jim Crow laws, the only way to have integrated access to a restaurant, swimming pool, or movie theater was to make private (i.e. members only) clubs. Obviously you are not correct on this one, as we now have integrated them with out resorting to such clubs as the means.
So also the opposite could occur.