California is an "at will" employment state. That means that any employee can be terminated at any time for any reason that is not against the law, discriminatory, or retaliatory.
A reason that is against the law would be, for example, terminating an employee for refusal to illegally dispose of hazardous waste.
A discriminatory reason would be one based on race, color, religion, sex, national origin, disability, or age; participation in schools or places of worship associated with a particular racial, ethnic, or religious group.
A retaliatory reason would be taking an adverse employment action because someone filed a complaint of discrimination based on race, color, religion, sex, national origin, disability, or age; participation in schools or places of worship associated with a particular racial, ethnic, or religious group.
If you would like more information about this, it is available at the Equal Employment Opportunity Commission's website, www.eeoc.gov.
That means that an employer can implement policies such as a "no gossip" policy, employer can terminate an employee who fails to follow that policy.
I am sorry that I don't have better news for your friend about this - especially since talking about the type of car that someone's spouse drives seems very innocuous.
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