As a journalist, I get dozens of press releases in my email inbox every day.  One of the oddest press releases I recently received was from a group that was calling for a boycott of a popular Greek yogurt brand, because even though the yogurt doesn’t contain genetically modified (GMO) ingredients, the cows providing the milk may be eating GMOs.

Now when you start picking on Greek yogurt, one of my favorite foods, I start to get annoyed. But I also start to wonder: Should I be worried about eating GMOs or serving them to...