It seems to be limited to a few barns on the peninsula - Rancho Viejo, Portola Farms and PVTC, although you could pay extra to have hay fed at PVTC. RV feeds hay cubes, PF and PVTC feed hay pellets. I can’t remember whether the no-hay thing was also the case at Webb Ranch and Springdown. It was not the case when I boarded at the Horsepark, our horses all got hay.
It is because the folks that haul off the manure/shavings for those particular farms use it as compost and do not want hay mixed in due to the how long it takes to degrade and the possiblity of grass/grain/weed seeds remaining in the hay.
I haven’t lived in the bay area in well over a decade, and I’m honestly surprised it is still the case.
Back to the original poster - Lindsay and Matt Archer are a good option.