I have a hairy mushroom and my goby rests on it all the time. At first, the mushroom would react and curl up and the goby would move away, now, about a month later, it doesn't move at all when he "lays" on it.
I believe when I got mine it stated that they should be 4-6 inches away from other corals.
Not sure about how much sting they have however, the other day, one of my large Mexican Turbo snails was cleaning under/around it and all of a sudden the snail dropped to the bottom of the tank. I uprighted the snail and he didn't move for a couple hours..it reacted like he had been stung. I'm not sure if that's what happened but it sure seemed like it. Kinda funny that he hasn't got back to that area since.
The goby still hangs on the mushroom every day and the mushroom appears to have grown almost 2 inches in the month I've had it!