Iguanas are not equipped to hunt down and digest animal prey. Their digestive system employs a hindgut fermentation process, which is to break down plant matter, cell walls and carbohydrate. This isn't to say they couldn't digest animal protein, but just that they're optimised for plant matter. They also spend their entire time in the wild living on their food plants. So, my conclusion that they are strict herbivores still stands.
Some people seem to have almost converted their iguanas into carnivores.
However, iguanas are nothing if not opportunistic. This suggests that even in their native habitat they might resort to limited omnivory if that becomes necessary for survival. Iguanas in captivity are nothing if not stressed, and offered poor quality diets on the whole. Therefore, eating insects, mice or whatever doesn't seem unreasonable. Iguanas will happily eat their substrate if nothing else presents itself.