Bob, you mentioned that your Dad peeled mushrooms, I have never peeled a mushroom, nor have I ever washed them, just a gentle wipe with a paper towel maybe, how about everyone else?
Have memories of my Dad peeling mushrooms (and I forgot cutting off the stalks), mainly because apart from this Sunday morning ritual and the cooking of the Breakfast, Dad never took part in any kitchen chores. As for the subject of 'to peel or not to peel' that topic has come up many times before in the family and with friends. All variations mentioned cropped up, but none changed my engrained practice (nor I believe my sisters) to peel mushrooms and de-stalk them.
Then I got married.
My first marriage was to a country girl and at first I lived with my in-laws in a lovely rural village and everyone picked field mushrooms and I was shown how and where by my father-in-law. So every Sunday morning I had to accompany him very early - did I say VERY EARLY - as he rose at 5 am 7 days a week (5 of the days he also held down a job and liked to spend at hour on his small holding before setting off to work) and so at around 5.30 am I was expected to go with him ... ON A SUNDAY MORNING!! Her mother would always wash the mushrooms and dry them, but have no idea if they were peeled or destalked. I recall asking my wife to peel ours and remove the stalks.
My second wife came from Northampton and a townie and she had never really like Mushroom, has no idea how they were prepared, but does remember they were field mushrooms. These were picked by her father (often accompanied by her) when he visited his sister (married to a farm labourer). His sister lived 'out-in-the sticks- even more remote than my former village - and one crossed fields to reach their tied cottage. She has some recollection of her mother washing and drying the mushrooms, but not of peeling and thinks they were also de-stalked.
Moving on further and living in Kent in an urban setting, no more picking of field mushrooms (at least not by us) so, because I liked mushrooms, they were bought either from a greengrocer or from a weekly market stall. My wife followed the routine passed on by me, to wipe, peel and de-stalk. Later when mushrooms were sold a-plenty at Supermarkets, they were (or looked) clean enough to bypass the wipe routines, but by and large they were wiped, and yes peeled and stalks removed.
As I said earlier the subject of how we prepare mushrooms as cropped up many times. Generally my sisters followed the same rituals we learned from watching Dad but we have all experimented with not peeling and even using the stalks either eaten with the mushrooms, or added to greens water, brought to the boil, and used to make the gravy.
So to conclude I still peel mushrooms and either find a use for the stalks or discard them with the peel.
And the mention of runny poached eggs ugh!

almost sent me running to the bathroom. Runny yolks ok but runny whites, no thanks
I am surprised my narrative would conclude you to think I meant runny whites - no always runny yolks every time. The secret is to know when to lift out the eggs from the vinegar water.
Mind you I know plenty of people my wife included who will not touch even a faintly undercooked white of an egg however cooked and in the past my friends wife when staying with us would always ask for her fried egg to be well done. My interpretation of this (copying the American 'Easy-Over') failed and it took several tries before I could produce a 'well-done' egg that met her standards. (As far as I was concerned you could have soled your shoes with the end result).