@Diane G. A little late to the game on this one... I'll save you an additional opinion and just call out that what @Elliot Blanford and @Account Closed said are correct in that what you are doing is discriminatory, but not based on any protected classes.
Whatever criteria you use for screening applicants needs to be applied consistently across all applicants and within the context of any existing laws both local, state and federal. And that is not just protected classes but other areas like source of income. (so Sue's comment about the $50k is not discriminatory as long you apply it to ALL your applicants)
To answer your original question, the law you are looking for you can thank Jane Kim. She sponsored a bill when she was on the Board of Supervisors back in 2015 that passed and updated the SF Rental Ordinance to include provisions around occupancy limits.
In summary your PM is right. To not accept them is just a gamble on whether or not you think your applicants are not savvy enough to know they can sue you, and that is a gamble I would rather not take in a place like San Francisco.