Personally I don't have a huge issue with ingesting GMOs; the issue stems from the fact that I would like to know that I'm ingesting them. As it is currently, in the United States, food companies are not required to label their products to indicate that they contain genetically modified organisms.
The only reason I wouldn't support this is that we live in a society with very poor science education, and as soon as it no longer becomes economically viable to research genetically modified foods (For example, as soon as they're labeled and people start to stop buying them out of fear and misinformation) the research on genetic engineering will stop. This is a problem because while starvation isn't a huge issue in the US, many developing countries are working towards solving their starvation and malnutrition issues by genetically engineering foods. Not to mention that it would essentially halt research on edible vaccinations, which have the propensity to eradicate many infectious diseases decades faster than the intravenous variety.
Furthermore, GMOs and non-GMO crops are substantially equivalent, making the label completely pointless. If you consume a GMO crop versus a non-GMO crop, no medical scan/blood test or any other exam you can think of would be able to show that you consumed that variety. It's essentially like forcing people to label crops that were raised 'with love' versus 'without love'.
Some GMOs are bad. Generalizing about pretty much anything that isn't 100% fact is dumb.
I don't think you've read any of the literature on GMOs, and you're just trying to make a false-compromise so that you can seem friendly to both sides of a controversy.