The California Department of Motor Vehicles says:
There is no need to rush into a DMV field office. Until October 1, 2020, a valid California driver license or ID card can be used for federal purposes, including boarding a domestic flight and entering military bases or secure federal facilities. After that date, only a REAL ID card or other federally approved documents will be accepted, such as a U.S. passport, passport card or military ID.
However, the U.S. Department of Homeland Security says (in combination with here):
California has an extension for REAL ID enforcement, allowing Federal agencies to accept driver's licenses and identification cards from California at Federal facilities, nuclear power plants and federally regulated commercial aircraft until October 10, 2018.
...
When a state's extension expires, the state is subject to the statutory prohibition against Federal acceptance for Federal purposes of the state's driver's licenses and identification cards.
2018 is not quite 2020, so I guess the question is obvious... which government is lying?!?
Update (January 2019):
In November, questions emerged about whether the state’s REAL IDs were compliant with federal regulations and whether the agency could meet a Jan. 10 deadline for certification. The Department of Homeland Security on Wednesday granted the state agency a last-minute extension to meet those requirements, despite the government shutdown, extending California’s deadline to April 1.