I've been spraying a copper and sulfur mix about once a week during bloom season. Copper soap (copper octanoate) and micronized sulfur are both OMRI listed (ie, organic) products. And with a mister, the amount of product needed is miniscule (I can cover my entire grove of ~30 mango trees -- some 20 feet tall -- with under 2 gallons of mix). So the potential for copper buildup is essentially nil, and in the case of sulfur is not even a concern.
I haven't been paying attention to bloom cycle, and I haven't noticed any detriment by spraying open flowers. I also haven't found any literature suggesting that it's harmful (most literature suggests spraying at regular intervals, eg, once per week without regard to bloom stage). I do however, spray at dusk, as both products have the potential for phytotoxicity.
Like Gary, I too was initially averse to using any sort of "chemical" to control fungal issues. However, in talking with Har and researching the topic, I've come to realize that the use of "bio-sensible" products (as Har calls it) is essential to maintaining a healthy and productive orchard. At present, the only 2 "chemicals" we use are copper soap and sulfur, and their use has had a dramatic impact on both tree health and production.