you're probably OK as long as your rules are consistent. a specific credit score or number of missed payments is a fine cutoff and not discrimination unless you are making up the rules on the fly.
the thing about discrimination (by family status or anything else) is you can't have tougher application rules for that category of people, and you can't make their lease terms tougher like requiring a bigger deposit.
In my state source of income is protected, see below. IDK about other states.
If it is legal where you are, I still think you should be careful not to require sources of incomes that are really a signal of family/gender/marital status. Ask yourself honestly, would you accept other people living off savings? maybe a single guy going back to school for a year? maybe an author who took an advance? maybe a childless couple who sold their house to travel and wants to live in your town for a year for some reason?
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https://www.dfeh.ca.gov/Housing/California law protects individuals from illegal discrimination by housing providers based on the following:
Race, color
Ancestry, national origin
Religion
Disability, mental or physical
Sex, gender
Sexual orientation
Gender identity, gender expression
Genetic information
Marital status
Familial status
Source of income
Citizenship*
Primary language*
Immigration status*