It’s ridiculous that in this country your gender can be invalidated not only by crossing state lines, but by being born in an inconvenient state. I too live in San Francisco but was born in a state - Pennsylvania in my case - that currently requires surgery to change the sex marker on birth certificates. I have no desire to have surgery at this time, but if I did, it would not be to “validate” my gender identity for the government or public’s benefit, it would be to alleviate dysphoria for my own well-being.
Fortunately, I have the privilege of access to a trans-affirming doctor’s office, and was able to get all of my IDs changed over without ever producing a birth certificate. Including my passport, though the passport office did give me some grief as I went there before I had my new state ID (I don’t drive). I needed to spend several hundred dollars to have a court hearing, then have my name and gender change published in the paper; fortunately publication is no longer required (in California) as of July 2014. Then I used my court order to update my Social Security record, which allowed me to get a new state ID and passport without needing to update my birth certificate.
I’m not planning to rip up my own birth certificate even though I no longer relate to the name or sex listed on it, but I’m not stealth and am not currently seeking employment or expecting any other circumstances that would require anyone to see it. The same applies to my school records. But that’s only me; all trans people should have the right to change their identity documents without undergoing invasive questioning or procedures.