The Washington Post contains an article on a recent survey by Oklahoma State University where over 80 percent of Americans support “mandatory labels on foods containing DNA,”
The Oklahoma State survey result is probably an example of the intersection between scientific ignorance and political ignorance, both of which are widespread.The most obvious explanation for the data is that most of these people don’t really understand what DNA is, and don’t realize that it is contained in almost all food. When they read that a strange substance called “DNA” might be included in their food, they might suspect that this is some dangerous chemical inserted by greedy corporations for their own nefarious purposes.
The article discusses the wider issue of scientific ignorance driving policy decisions, and there is some further comment at io9. A summary of the full survey results is available (PDF).
FWIW, DNA tests have frequently found that fish sold are often not of the species claimed. Whether this is important to you or not, fraud of this nature is common.