Disorders such as celiac disease, Crohn’s disease, rosacea, and eczema—all of which involve the skin, the immune system, and the gut—reveal just how intertwined these systems are.
As I noted a couple of days back, the so-called "immune system" is not a distinct, identifiable, separate set of organs and the skin's job of keeping out invaders makes it part of the immune system.
https://news.ycombinator.com/item?id=24015957
I will add that skin and gut tissue are both the exact same class of tissue: They are both epithelial tissue. So it should hardly be shocking that when one of your epithelial tissues has an issue, so does another.