My husband and I are not overly picky about what our son eats, so long as it's relatively healthy (i.e. "better than a Happy Meal"). We don't care if he ingests soy products, or milk that doesn't come from organic, grassfed cows. There are two things about which we are pretty strict, however: no red meat, and no juice.
There isn't any sort of moral issue with the red meat. It's just that, for health reasons, my husband and I don't eat it so it's not kept in our house. So our son is not used to eating it, and if he does, it'll give him the runs.
We also don't want him drinking juice because his pediatrician told us it has very little nutritional value and is more sugar than he needs. Since he's not used to it, juice will also give him the runs.
A lot of our life decisions revolve around messy-diaper avoidance.