Some species of Asterina are harmless film algae eaters. Others are coral munchers.
*Usually* the muncher type gets a bit larger, and they may have red and/or blue on their backs, in addition to the tan/off-white. The harmless ones are usually off-white/tan in colour.
Just because it's traveling over something doesn't necessarily mean it's going to eat it. Do keep an eye, remove it if its activity is suspect.
In my experience, I've only known a couple of people that ended up with the harmful kind of Asterina - and they were a scourge, but the vast majority are harmless.
Jenn