Well at least for now California's law for background checks on ammo has been blocked by a court in all places California.
They also mention about the importing ban on ammo from other states violates the federal interstate commerce laws.
www.foxnews.com
They also mention about the importing ban on ammo from other states violates the federal interstate commerce laws.

Judge tosses California law requiring background checks for ammunition
A federal judge blocked a California gun law on Thursday, that required people to undergo a background check before purchasing ammunition.