Under Federal law, it is illegal for a landlord to arbitrarily discriminate against a protected class. In California, such discrimination is an affirmative defense in an unlawful detainer (eviction) case.
The Fair Employment and Housing Act -FEHA
Under the Fair Employment and Housing Act (FEHA) it illegal to discriminate against any person based on any of the following protected classes:
*Disability - Disability includes but is not limited to both physical and mental disabilities
*Familial Status - Familial status means that one or more minors live with the discriminated individual, or that individual is pregnant, or is in the process of securing legal care of a minor.
Acts constituting illegal discrimination
Acts constituting illegal housing discrimination include but are not limited to:
Owner occupied exception
When a Landlord rents space in an owner-occupied single family dwelling, to no more than one individual, then that owner may choose to not rent to any person based on any characteristic. However, it is still illegal to state a discriminatory preference in any rental advertisement - with the one exception of the right to advertise a preference for male or female.
Discrimination based on economic status
Remember that economic status is not a protected class. Thus a landlord may discriminate based on income and/or credit history. However, a landlord may be in violation of federal and state discrimination laws if he/she have different financial standards for different members of a protected class.