I usually look at all the gunk on the mushrooms, and knowing they're grown in a chicken poop mixture, wash them anyway. Probably not better than a good wipe but I can't help myself.
Rinsing them is absolutely fine. The "food science" recommendation around cooking mushrooms has changed in the last few years. Many cooks are seeing good results by starting to sautee the mushrooms in water and only cooking with oil once the water has boiled off. This enables the air pockets to collapse and for a lot of the moisture to evaporate so you end up needing significantly less fats. I've switched to this method myself, and I've been very happy with the results.
Might well depend on the species as to which conditions are most favorable, but AIUI most of your farmed mushrooms are grown on other-than-poop substrates: grain, straw, wood and wood pellets, coffee grounds, shredded coconut husk.
Probably still a good idea to clean them off, though: none of those other things are particularly tasty :)
Most mushrooms you eat aren't coprophilous fungi. You're probably thinking of some variants of magic mushrooms (not all magic mushrooms grow on dung).
The mushrooms you're eating grow from the dirt. If you're into mushrooms, you'll probably also have mushrooms that grow on trees. But unless you're looking to trip, you're not getting poop shrooms.
