Hi RiiSi - My Dogue de Bordeau does, and all dogs at the stables do. Fillies & colts tend to eat their mother's manure from time to time, too. I'm told that they do this for the nutrients & probiotics that the manure contains. Once my DDB enjoyed a bit too much of it, & vomited an entire manure pile onto my kitchen floor! �� I now make sure she's not hungry before we go there.
My DDB does have skin issues. I'm currently treating her for demodex, & she has gotten hives during spring/summer months from various grasses. I hadn't thought to link eating manure w/ skin conditions before seeing your post. The allergies were exhibited prior to my ever taking her to the stables, but the demodex seems to have started after.