According to the school's history page they clearly were established as a Catholic school in 1850. The claim that they were established as California's "first independent and first Catholic" school smacks of revisionism. I suspect they were simply a Catholic school originally. The published "history" makes no specific note of when they dropped their Catholic affiliation or whether they simply decided to "expand" their identity to include open apostasy.
I remember this happening about a dozen years ago in the Archdiocese of New York; after Hillary Clinton spoke at a “Catholic School” (Marymount Manhattan?), the archdiocese indicated they were no longer Catholic (and they completely agreed). Here in NJ our Catholic schools (those remaining) are circling the drain; a small number will survive for wealthy people (and they’ll be required to take on non-Catholic tokens to be diverse, all on scholarships). The rest will be rented out/sold.
My town had 6 Catholic schools 50 years ago; now we have none.