First, it's a bit of a red herring, the biggest issue IMHO is the synthetic pesticide use which correlates it. Many plants are primarily GMO to make them pesticide-resistant. The issues with pesticides you may be aware of.

Another issue is that often GMO correlates with patentry, terminator seeds, IP lawsuits, and so on. But that's also a tangential issue.

The main issue is that, just like anything new, it puts us in the "beta testing in production" area, where the product being tested is "things which none of our ancestors have ever encountered, evolutionarily" and production environment is "our bodies".