If they are flatworms they will move around. It should only take a minute of staring at one spot to figure out. Plain red mushrooms will definitely develop more colorful characteristics over time too so could be a very god thing.
I haven't had a lot of experience dealing with flatworms, so please excuse my ignorance lol. But I thought flatworms would change colour to match there host as a camouflage technique? Shouldn't the flatworms be red? Or atleast turning red?
Acro eating flat worms will take on a mottled color tinted like the host. Aefw are a plague.
Those look like planarian flatworms. They aren't really harmful unless their numbers become problematic. Many wrasses will eat them.