Joseph, you didn’t answer my question about davening in a MO shul.
LB, married men who wear black hats generally remove them when they enter shul for shacharis since they don’t wear them with a tallis. Sometimes they do get mixed up.
Tuition, your MB quote is very interesting since hats are generally not worn these days. In the old days, every downtown (remember those?) had a store that specialized in men’s hats.