How sound is the saying that it is impermissible to hang clothes in bathrooms because devils inhabit them?

Bathrooms are shelters for devils, so a person should not stay in them except for the necessary duration.

The Messenger of Allah, peace and blessings be upon him, said: "Indeed, these privies are attended [by jinn]. So, when one of you goes to the lavatory, let him say: 'I seek refuge in Allah from the malevolent and femalevolent (jinn).'"

"Privies" (الحشوش) refer to places of defecation, and "attended" (محتضرة) means that they are in the presence of jinn and devils because they are places where one's nakedness is exposed and the name of Allah is not mentioned.

It is desirable to avoid places of Shaytan.

As for hanging clothes in bathrooms, it has no relation to the dominance of devils; that is a false claim and a superstition.