While there does not seem to be a lot of official action by the Green Party on GMOs, there is a lot that California Greens should be doing.
There is a non-profit group called Californians for GE-Free Agriculture. This is a coalition of many organizations who recognize the dangers inherent in releasing the genetic material from Monsanto and its cousins into our environment, which un-regulated GE use will surely do. Make yourself familiar with this group and pay close attention to the ACTION page.
The second is to find an support those who would highlight this issue and to defeat the proponents of un-regulated GMO use in Agriculture. This includes the following sponsors of California SB 1056.
Principle Authors: Assembley Members Matthews (AD 17, Tracy) and Maze (AD 34, Visalia)
Senators Cedillo (SD 22 - LA) and Denham (SD-12 Modet0)
Assembly Members Arambula (AD 31, Fresno), Calderon (AD 58, Montebello) , Canciamilla (AD 11, Martinez), Cogdill (AD 25m, Madera) , Garcia (AD 80, El Centro), La Malfa (AD 2, Redding), Negrete McLeod (AD 61, Ontario), Parra (AD 30, Bakersfield), Plescia (AD 75, San Escondido), Salinas (AD-238, Salinas) , Torrico (AD 20 Fremont), and Villines (AD 29, Fresno)
What strikes me as unusual about this is the number of Hispanic legislators from districtes without substantial agricultural interests, who have signed on as co-authors. I don't see any with an active Green opposition other than Maze, who is being challenged by David Silva this term.