You raise an interesting question, which has never actually been considered by a California court.
Federal law prohibits discrimination in employment based upon race, color, nationality, religion, sex, age or disability. California's list of prohibited classifications is much broader: race, religious creed, color, national origin, ancestry, physical disability, mental disability, medical condition, genetic information, marital status, sex, gender, gender identity, gender expression, age, or sexual orientation.
Among the California list is the term, "ancestry." No California or federal court has clearly defined the meaning of this term. One court described "mexican-american ancestry" as unlawful discrimination. However, the court did not define "ancestry" -- it merely commented on the specific issue before the court.
It is well-established in law that where the legislature fails to define a particular term, the court is required to use the "plain and ordinary" meaning of the term. And, the term, "ancestry," per Merriam-Webster's online dictionary is defined as "1. Line of Descent."
The clear meaning of the term would make a refusal to hire you based upon your father's prior employment as discrimination based upon your ancestry, since you are obviously your father's descendant. If I were the judge considering the matter, I would hold that you are indeed discriminated against based upon your ancestry.
However, as no court has ever been faced with the specific question, you could have a real fight on your hand -- because there will be strong resistance to expanding the potential classes of unlawful discrimination to include direct descendants of others.
Nevertheless, if you want to see what the government has to say about the issue, then you can file a complaint with the Department of Fair Employment and Housing
(DFEH), and see what happens.
Hope this helps.