First of all, please note that genetically modified organisms (GMO) are not banned in food in California. As this link will show, Californians rejected an initiative just this past November (of 2012) that would have required that all GMO food be labeled. This makes it clear that it is legal to sell such food in California. There is at least one county in California that has banned GMO food, but the state as a whole has not banned it.
There are two main reasons why some people want GMO food to be banned. The first is the possibility of environmental harm. Many people fear that GMO crops will interbreed with wild plants. They fear that the genes from the GMO plants will harm the wild plants in ways that cannot be foreseen. In addition, many people worry about the health effects of GMO food. They worry that eating such foods might change or affect our bodies in ways that we cannot foresee. They point to the concerns over the amount of steroids and antibiotics in the animals we eat and argue that GMO foods could be similarly dangerous.
Although many people have pushed for bans or labeling requirements for these reasons, California has not banned GMO food.