They don't actually eat the coral. What they do is suck the slime off of it, causing it slime more, and damage the area they are sucking on, they can kill an entire colony.
Went through this a number of years ago. Gobiodon citrinus are obligate corallivores. Had one around 2006 that went through a handful of newly-placed frags before I saw what was happening. Did some research, and came across a study that examined the gut contents of a sizeable sample in the wild and over 90% was coral polyps. Unfortunately nearly all research these days is behind paywalls, but here are few links, one paywalled the other not:
Diets of coral-dwelling fishes of the genus Gobiodon with evidence of corallivory
Download the full text pdf format for access to the paper.
This one actually lists acropora as 99% of the stomach contents.
Search for "Gobiodon citrinus" around page 90 (or ctrl-F and fill in "Gobiodon citrinus" to search).
Of note also is the toxic mucus it produces as noted here: