In Medieval Islamic societies it was actually the opposite.

"Al-D̲j̲āḥiẓ maintained that such [skin] ailments are not social stigmas but are what may be called signs of divine blessing or favour. The afflicted were spiritually compensated by God and special merit should be attached to their lives. Thus he countered the contrary opinion that the infirm should be disparaged or satirised for their afflictions. Most of the poets quoted by Ibn Ḳutayba also appear to say that skin disorders should not be the cause of scorn and revilement but should prompt the sufferer to repentance."

Islamic medical practice was sufficiently advanced to distinguish various types of skin ailments. The above was written about the much more serious forms of leprosy, necrosis and the like, so there was obviously tolerance for diseases far beyond acne.

That said the Arabs had a habit of giving a laqab, or nickname, based on physical appearance or attributes. Thus the name "al-Djahiz" itself (usually spelled "al-Jahiz") refers to the fact that he was apparently sort of bug-eyed. These nicknames could be given ironically, however, hence you have beautiful women with nicknames like "the hideous" so a person given a nickname in regards to their complexion might well have a skin issue or it might simply be ironic.

See the entries in the encylopedia of islam on Leprosy ("djudham") and "lakab."