IME, mushrooms can cause damage to fleshy stoney corals. Although mushrooms don't have sweepers, I have often seen flesh retraction and then exposed skeleton at points of contact between many of the fleshy stoney corals listed above and mushrooms.
Any mushrooms on the glass should be easy to remove (and maybe recycle to your LFS for credit), and even in smaller tanks you can do the kalk injection (which can be effective in killing all sorts of unwanted growths), as long as you limit how many mushrooms you inject at a time.
I don't know what your lighting is, but both hydnophora and galaxea corals have very powerful stings, so those are both possibilities as well.
Finally, I've found that green star polyps, once established, have chased most of the mushrooms off their rocks (the mushrooms have the "choice" of either bailing off the rock or being overgrown). Of course, you then have the problem of stopping the GSP growth, which can be as bad as (or worse than) the mushrooms.
FWIW,
Kevin