And that's my main complaint with transgenics, which perhaps we should use that word instead of GMO. We are not exhibiting an 'abundance of caution' in this work.
We have major illnesses crossing over from birds and pigs all through our history. Some pretty bad ones in recent times. Moving genes between these species (which we are doing, to try to make more pig organs biocompatible with humans) could be very, very bad. Do we have a good model for what gene groups can increase the likelihood of viruses crossing between species? If this information exists they should be shouting it from the rooftops. But they aren't, which suggests that no such practices are being observed.
If the next H1N1 turns into the Spanish Flu, 'I told you so' just isn't going to cover it.
If someone wants to take a juicier tomato and a tomato with more flavor and combine them to make a hybrid tomato, I don't so much care about a genetically modified tomato that could have eventually been hybridized in the greenhouse. As things get further from that, I have more reservations and I think we should look a little closer. Across species is a little more concerning. Across families moreso still, and so on as we talk about bigger and bigger jumps.
You make a good case about our own genetics specifically, too. Things that alter our DNA or the DNA of things we already share diseases with (other primates, horses, hogs, for example) should probably get more attention to possible risks and side effects.
But I do recall there was one type of genetically modified corn that was made to produce a specific chemical that caused insects' stomachs to explode. Supposedly it was there to reduce the need for pesticides. I recall thinking to myself, If it does that to insect stomachs, what would it do it animals' stomachs?
The other issue that we haven't fully gotten figured out is cross pollination concerns. Aside from the problem of Monsanto's suicide seeds that grow only once and can't be harvested again accidentally cross pollinating with regular seeds from nearby fields, there is another problem with people becoming legally liable for the actions of bees, butterflies and other pollinators. Some GMO's have unreasonably restrictive licensing. This has resulted in a person's field getting pollinated with by bees who were pollinating GMO plants from a neighboring field now getting sued for having plants they haven't licensed even though did not originally plant that particular variety.