In the tech world and scientific communities, no. We care about IP abuses, if anything--many, many studies have shown that the products are safe to eat, but Montanto's behavior is occasionally despicable.
The rest of the country, though? The hippie, New Age folks that make up a frighteningly large segment of the population? GMOs are "unnatural Frankenfoods" destroying our DNA and whatnot.
My friend group is definitely skewed toward the hippie spectrum, so I may me over-estimating their numbers, but only 37% of Americans say GMOs are safe to eat[1]. I don't know what percent of those know who Monsanto is, or what percent say Monsanto's business practices are unethical, but I certainly lean toward "designing better corn" being the most common qualm.
The problem with GMO's is that most people aren't equipped to have a nuanced discussion about them so the conversation devolves to massive generalities and extremes that aren't useful because both polar extremes turn out to be illogical positions to take, but they are the only two positions that are discussed.
As far as I can tell, the only reason people have issues with Monsanto specifically is because they are explicitly named in Food, Inc. If it were about GMOs or pesticides, there are many other companies, and even larger and more well known companies, that are developing similar and potentially damaging products.
The audacity of designing a better corn seed knows no bounds!