this is a hard one... have you seen them actually pick pieces of the polyps off?
tangs will commonly pick at the base of the rock under the polyp looking for algae. this may look like there picking at the polyps, but usually there not
im not going to say its impossible, but its VERY uncommon for either type of these tangs to eat polyps
__________________
Show people you appreciate there advice, click the icon under there name and give them Reputation points
it is still more likely from my experience, that the tangs may be picking at algae or detritus between the polyps or even cleaning the rock of decaying polyps... than actually eating it. i think your polyp population decline may not be the fault of the tangs.
i may be a bit late on this thread but i may be able to shed some light on this issue for you or others with simular problems;
tangs(all species)and sergeons are natural grazers in the wild their main function in life is to eat and breed..ok and poop alot lol..they eat at almost every waking moment
anyways in captivity these species keepers(hobbiest) tend to not realize the natural behavior of these fish prior to purchasing them hense one of the main reasons tangs are ich magnets.. or aggressive and can be pickers of corals.. there is nothing wrong with your fish per say except the fact they are hungry and if the foods they are being given are not nutrient satisfying they will search elsewhere (your corals) these fish should be fed a nutrient enriched diet at least 3 times per day minimum..more if you can new arrivals and small tangs should be fed 5-8 times perday to reduce the risk of paresitic infection.. if your fish begin to get the nutrients they need more often in small amounts per day you may find them to be less of a nuisance to the other inhabitents of your tank.. i hope this helps..
ps herbivores require 75% plant and vegitation and 25% protein in their daily diet.if this requirement is not met you will shorten the life span of your fish.