Anemones move, as such they can move onto things that either hurt the anemone or animal they move onto.
Personally over the years i've lost or had sever injuries to many of corals due to anemone movements. Including one near tank wipe out from a MP40 that an anemone crossed with. Basically resulted in a blender of anemone bits all over everything. Wiped out 70% of the livestock including the fish before I could contain and begin the healing.
So to put it mildly, reef safe..... no. With extreme caution is a better way to put it.
With that, most people have them in their reefs. Its hard to ignore the beauty of the symbiotic relation of a clown and its anemone.