A landlord is legally required to follow fair housing guidelines. Failure to do so can result in some pretty hefty fines from the state as well as law suits from perspective tenants...all sorts of nastiness.
Some states require that you disclose why an application is not accepted (the ones I have worked with do anyway). I assume some states may not make that a requirement.
The only exception may be if the landlord lives on the property he is renting, such as small multi-unit setup like a duplex or four-plex. In those situations, some states (perhaps all) allow the landlord complete discretion on who they may rent to regardless of protected class. However, before relying on this exception, a landlord should check their state statutes.