This is called "freedom of association". If you are a deeply religious apartment owner, you should be free not to rent to an unmarried couple or a homosexual couple, or anyone for that matter. It's your private property. Now, having that attitude may put you out of business (either through lack of clientele or protesters out front), but that's your decision.
Does this, should this, include blacks? Read what Walter Williams has to say about that in Economic Straight Thinking, an excellent article.