I don't know of a good site or even names for the common mushrooms that are definitely OK, however, any mushroom that does not have little tentacles should be fine (there are only a few, usually
red/orange,
blue or pink - could not find an image but they look like the red and blue with an almost smooth surface).
Ricordea fall a bit on the iffy side. If you want to try leaving them in the tank, pay close attention to the octopus when it climbs over them (much like you are doing with your starfish - not sure starfish can feel the stinging though). If you see a react, then rehome the coral. Sometimes you can place a mildly stinging animal in a place the octo doesn't venture but this is difficult to second guess.