When changing my own kids diapers I never wore any gloves when changing their wet or poop diapers.
I just washed my hands after changing the kids diaper and washed my hands afterwards especially if I got poop on my hands.
I've gotten poop on my hands when changing my kids diapers but that never grossed me out and it was just my own kids poop.
As for daycare when I worked at daycare before having my own kids I had to wear gloves which was a rule we had to follow.
Even for pee diapers we had to wear gloves and then we had to change the gloves when we changed another kids diaper.
I also had to wash the kids hands and my hands between diaper changes.