Not sure which shoe question is for which exactly, but here goes.
I will wear my perforated black suede slipper shoe (essentially a loafer) with thin black socks in cool weather and with nude knee-highs when I want to give the bare/perforated look. And I wear my oxfords with and without socks (whether "acceptable" or not) but when with socks, I'm wearing them with pants that work so that the oxford is almost like a bootie and covered up. When I am wearing my version of a skinnier tapered pant, even though I wear them full length there is a lot more vamp showing, so I tend to like to wear the nude look. So I think the oxford for sure could be worn with a matching thin dark sock or with nude hose for a more open look.
The other shoe is maybe a cross between a pump and a loafer? So that may be pants- and wearer-specific. The more it is used like a heeled loafer, with a trouser or bootcut pant , the more I would wear it with a thin sock (if it fit properly). If you read Corporette, there is a lot more discussion of, and tolerance for, a standard "heeled loafer" or such worn with a trouser sock by women in serious professional dresscode jobs that still need some semblance of foot comfort (and good sense) not achieved by a stiletto pump. Some of these folks are not at all doing the ankle pant/bare leg thing.