For shared vans, Bayporter Express charges about $40 between SFO and Richmond or Oakland (but I don't know whether they'll go between SFO and OAK, or if there's some reason that they wouldn't). IME, they've been pretty reliable, but all bets are off during strike-caused gridlock. The Bay Bridge will be worse than hellish, whether you go by van or rental car, so some of the circuitous suggestions made above may actually work out better.
There's an SFO-Walnut Creek shared van, East Bay Connection, but I have no personal experience with them.
I assume that either van reservations or rental cars will be much harder to come by than normally.