My cat wouldn't jump up onto the soap table with me working at it either, but I have been known to accidentally splatter raw soap on the floor and on the throw rug upon which I stand and onto my own feet. My cat often rubs up against my legs and obviously walks on the floor, so I don't want her near my soapmaking. Accidents happen and although I can quickly clean up my own self, I don't want to have to handle a lye burn on a cat!
In fact, the last time I splattered soap onto the floor, I stopped soaping long enough to cover a spot on the throw rug with a towel & wiped the floor with vinegar to prevent the possibility that Kitty Baby might later wake up and come get raw soap on her little toe beans. I think I also had to wash my feet, which has only happened maybe 4 times in as many years, but I am well prepared for that. Immediately after molding the soap, the throw rug & towel went into the washing machine to ensure no bare toe beans or people feet would come in contact (Hubby also walks around barefoot.) There are no doors to keep Kitty Baby out of my kitchen, so I don't soap while she is awake, but there is no guarantee she won't wake up, so I am pretty cognizant of possible spills and splatters. Usually I prefer her to be outdoors or on the Catio (which does have a door I can close.)
True, I rarely wear sleeves and neither do I wear closed-toed shoes (just not my thing, even in winter, I only wear zorries in the house, maybe with socks if I'm cold enough), and I see that I do show my bare forearms in at least one soapmaking video, but not my almost bare feet.
I agree that some soaps are more fully saponified before the 24 hour mark than others, but that is not always the case, and some soaps are ready to cut in as little as 8 hours, so I would not trust that saponification is complete that early. Personally, I do believe wearing gloves when handling soap while unmolding and for at least the first 48 to 72 hours is prudent. But then, I also use a very low SuperFat, so perhaps it is relative.
I don't think the intent here for this thread is to be overly critical of other soapmakers, but to draw attention to the fact that it's not only the experienced soapmaker watching these videos, but the novice who may not realize that some of the practices we may feel safe for our own selves, is not what we preach to the newcomer.