Organic to me is a buzzword in many circumstances. One of them is in using copper.
As Clark shared, copper CAN be extremely toxic for aquatic life and literally to the trees attempting to be protected.
That said, properly applied, it is a fantastic tool in the toolbox and accumulation to the point of toxicity in soils is unlikely when properly managed. But, it does do a good job of killing things, possibly including good things. That is one aspect to be weighed when choosing any spray, not necessarily just copper.
I say that with a significant arsenal of sprays I intend to utilize on an as needed basis myself, but basically more to say do your homework and see if other options might be acceptable for managing diseases and critters.