Not sure what the nuisance factor is for iguanas, but locally with the rock lizards they poop large poop and it stinks. One lady had them schooling up under a shed, and so much poop on her patio it was difficult to walk there.

One online article made it sound like they are innocuous, and only eat undesirable insects.

But the same lady watched them eat butterflies on her flowers.

And somebody saw one eating another of its kind that was dead.

No reason to think they don't raid bird nests, eat bees, and other things that should be left alone.

Larry