We tend to pick our own wild mushies so we peel em partly because things wee on them and partly because it's one way of making sure you haven't got a rogue one in there as the bad guys don't peel so easily. We always eat the stalks though.
What kind of person peels grapes?
We were on holiday, and a mother was feeding her child grapes while he was in the pool (he must have been at least 11). My OH was quite amused by this so asked her 'Why don't you peel them for him as well?' She replied 'Oh no, I don't do that any more.'
Mushrooms are a high percentage H2O anyway.
Wash, wipe, or just use, you probably won't spot the difference; although you might feel better about eating cleaned wild mushrooms.
I peel the big ones and not the small, Use the stalks of the small ones but not the big flat ones as the stalks tend to be woody. They make good soup though