Mushrooms do have the capability of stinging fleshy LPS corals if they're in direct contact with them (I've had mushrooms 'damage' leptastrea and afflict what looks like burns to blastomussa). In both of these cases when the mushrooms fully extended, they made physical contact with these LPS corals. Increasing the distance by another inch or two solved that problem.
I've had a mushroom which was attached to the bottom skeletal structure of a trumpet coral colony. As the colony expanded and grew in number, the cut off much of the light the mushroom was receiving. This motivated the mushroom to creep up to the top where it could access more light. However this manuever brought the mushroom in direct contact with one of the trumpet heads which it managed to eventually destroy (as well as inflict again what looks like burn damage to the adjacent polyps).
If the mushroom doesn't come within direct contact with the trumpet coral then the advantage lies with the trumpet, since they're capable of extending stinging sweeper tentacles several inches in length (this didn't work in the above scenario because the mushroom crept up from beneath the trumpet rather than from above or adjacent to it).
I've never owned bubble corals so I don't know were they would rate.
While they're fleshy LPS corals, acan's easily trump mushrooms. They can cast a web of their stinging mesenteries which can completely dissolve mushrooms and can reach out several inches away.
Bottom line: as long as the mushrooms do not come within direct contact with other corals they're usually safe. There are a lot of other corals which can out-sting mushrooms and sting from 3"-6" inches away. I generally place mushrooms in the 'low threat category'.
African cichlid and saltwater aquariums