That's what I do. It's not a carpet anemone so I personally wouldn't be concerned about the sting. Your mileage may vary though. Others are very sensitive to nematocysts, and cannot tolerate contact with any cnidarians. You can use a small piece of raw shrimp and see if it sticks.
Also, an anemone will react to touch very quickly while a mushroom is quite slow. One can take a clean stick and gently touch it to see how fast it retracts. The retraction can be trickier to judge if you don't have something to compare it to.