I have been following anti-GMO activists and the Monsanto haters for couple of years and here are some thoughts.
Anti-GMO beliefs are mostly on the left, which is unusual because the left tends to be more aligned with science, at least in comparison with the political right
These beliefs seem to stem from a few areas of activism: environmentalism, natural/organic movements, anti-corporatism, and surprisingly anti-war
The connection with environmentalism is pretty obvious. Agriculture does effect the environment in large and small ways. However most of the anti-GMO arguments tend to be about all modern agriculture and not specifically about GM-crops. It doesn't help that major environmental groups (green peace) promote conspiracy theories about GM crops.
Natural/organic movements: These movements tend to fall into the naturalistic fallacy, that is, natural good/man-made bad. These people also tend to romanticize more primitive times and see technology as stealing or corrupting the perfect human nature which they imagine existed when we were hunter-gathers. The problem of course is the natural things can be really bad and man-made things can be really good. Consider antibiotics vs leprosy. People who hold these views would have agriculture go back to 1900 where 90+% of people worked on the farm to feed 1.5 billion people; they would prefer to trap billions in hard labor and starvation.
Anti-corporatism is also pretty obvious. The idea here is that big companies are monopolizing food sources and driving the (romantic ideal of the) farmer out of business. However it takes a large company or university to fund research into crops (genetically engineered or not) and those organizations have been able to patent their research since 1930 (plant patent act) to recoup the costs. These big-ag companies generally do not farm, they are not monopolies, no farmer has to buy their products and their patents (such as RR corn and soy) expire.
The anti-war sentiment is pretty interesting and is tied to the anti-corporatism, which also coincides with the rise of the environmental and anti-corporatism movements. Generally the argument goes that companies that made products in previous wars are tainted and cannot be trusted with something as important as food. The most extreme version of this is the idea that companies are actively trying to kill people. This is relevant to agriculture because there were several Ag companies that manufactured Agent-Orange during the Vietnam war and are thus tainted by this argument. The problem is that the companies that made Agent-Orange were compelled to under the War Powers Act. They didn't invent it, and the certainly had no say as to when, where or how it was to be used. Additionally, the assumed danger of Agent Orange (surprisingly still unproven) was from a Dioxin contamination which the companies informed the government about... and were ignored.
Considering the sources of the anti-GMO sentiment you can see that it stems from the political and social movements in the 1960s. It is likely fostered by people who grew up in that time (baby boomers) and it will continue to be a major political issue until baby boomers leave public life. As it is, boomers are still a major factor in politics, education, activism and journalism... so I suspect that we will see strong anti-GMO activism for at least another decade.