The two seem to be polar opposites to me. In the case of vaccines, you have thousands of years of history that demonstrates the danger of diseases and recent history showing how effective vaccines are. Those arguing against vaccines need to show serious harm caused before it would cancel out the benefits.

In the case of GMO foods, history argues against the technology. We know that non-GMO food is healthy. We have thousands of years of evidence to support that fact. The problems GMO are solving are on the producer's side, not the consumer's.

You can argue that the problem being solved is providing enough food to feed everyone and that history also shows the devastating effects of famine and starvation, but there are other ways to solve that problem that have none of the risks of GMO foods (less reliance on meats, for example, would make much more efficient use of our agricultural resources). Show me an alternative way of dealing with measles, flu, tetanus, hep and all the other illnesses we vaccinate that's even half as effective as vaccines and I'll concede that the two debates are similar.

If you don't believe in the safety of "unnatural" foods, you'll need to stop eating corn, bananas, beef, pork, and any other domesticated plant or animal. Recent history has shown that GMOs are much more precise and effective at domesticating plants for our purposes.