Our house is largely wood floors. We have always been a no outdoors shoes in the house family (regardless of flooring).
I personally dislike walking around on hard floors in barefeet (plus my feet are always cold!) so I'm always wearing wool socks or slippers. That's probably the most ideal for wood floors. That said, I can barely keep my kids in socks and shoes when they're outside let alone in the house! So inevitably they are always barefoot in the house. We've never had much of a problem with it. Technically yes, the oils on their feet do leave some residue on the floor that can be visible after a while but I have to clean the floors way more often for other reasons for that to even become a noticeable issue.
If your family wants to do a house only shoes rule and it works for everyone I'd go with something like slippers. Super easy on and off and still super comfy.