I think you need to go re-read the Bill of Rights. Race is not mentioned in there at all, and religion is only mentioned insofar as it prevents Congress from making laws "respecting an establishment of religion, or prohibiting the free exercise thereof." It says nothing about being able to force people to associate with anyone else.
As for your question about WaMart, being able to do something and actually doing it are two entirely different things. They would not post a sign like that not because it is illegal but because it's bad business--ignoring the certain protests, artificially limiting your business is a mistake when you're trying to sell as much as possible.
Ummm. 15th amendment.
Section 1. The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of race, color, or previous condition of servitude.
Section 2. The Congress shall have power to enforce this article by appropriate legislation.