CBBs will eat feather dusters and similar. They may also kill or damage your clam. If they are hungry and are at home in your tank, they may taste-test other things, especially xenia. They gobble up aiptasia once they are at home in your tank.
I asked the LFS owner to show me that his CBBs for sale would eat. He fed mysis and I saw one of his CBB eat a couple. So I took that one home. Once in my tank, it would not eat mysis however, no matter what variety. I observed that all or nearly all the other CBBs in the LFS starved to death, and the LFS didn't stock any more after that.
Once in my tank, the CBB took out the couple feather dusters I had within a few days, but then wouldn't eat anything else, until I started buying live clams from the gourmet store that are intended for human consumption. These clams are stored in my refugium until I need them. I cut the muscle and pry one open every other day and drop it in the tank. The CBB has to share with an aggressive sailfin tang, and occasionally will take a chunk out of that guys fin (it heals within 4 days). So I spend about $7 per month to feed the silly CBB.
Not at first, but after a while, the CBB started on the aiptasia and made very quick work of it. Although my refugium is full of aiptasia, anything migrating to the main tank doesn't survive long.
The CBB is constantly searching the rocks for aiptasia and also pods I think.
Once or twice, the CBB has eaten mysis I put in. I have tried grinding and freezing mysis into a half clam shell, to fool him and teach him, but it thaws and slips out almost immediately.
If you notice unexplained flesh wounds on LPS, or your xenia is getting trimmed and you don't care for that, then increase the frequency of clam feeding. This might be taste-testing due to hunger. It would be a good time to change your setup, move your rocks around, and move that LPS to the refugium for a while, or to the other side of the tank along with the xenia.
Disclosure: 1 yr in hobby, 9 mos experience buying clams for a silly CBB