How Does Keynesian Theory Address Supply Shocks, Like the California Drought?
In what follows, I'm going to be very hand wavy - take with a grain of salt.

If you think about it, a demand shock is like a scenario of multiple equilibria (given the fixed levels of wages and prices):


If everyone is employed, everyone has a lot of income, can spend that on goods, and the demand for goods implies a large demand for labor, making everyone employed
If few people are employed, total spending is smaller, so is demand for goods and labor, corresponding to only fewer people employed


The Keynesian solution can be thought of as forcing the first case to happen rather than the second.

If you really have a supply shock, that is, lack of a factor important to production, there is no indeterminacy here. There just isn't that much (oil) available, increasing its price. The RBC spokesperson of your favor would say


  The high price stems from scarcity; both the high price, the low production and high unemployment are efficient.


In the standard problem, rigidity of wages and prices create inefficiency, they can be dealt with. Here, there is no such inefficiency, and no inherent solution to a supply side shock.