Soap irritates my facial and neck skin. By the 3rd pass, my neck and cheeks are on fire. Is there a shaving cream that does not have soap or is milder in the pH range?
Maybe it's not soaps in general but the fragrances in soaps. I can use most soaps but there are a few scents that cause a similar, but less extreme, reaction on my skin. I've found that cocnut (MW & Mike's) causes that; I can use other scents of theirs without issue, and heavily scented soaps like Mama Bear do that also.
My wife once bought me a tub of rituals samurai shaving cream and aftershave (2 in 1) and while it's never going to be a favorite of mine ( I like my soap and brush ) I use it when my skin is irritated and it works very good for that.