It appears that followers whose default outfit is clothing (that is, something without an armor value) refuse to equip alternative clothing, regardless of enchants on it. If your NPC friend has a barkeep outfit on him and you give him Mage Robe of Sheer Awesomeness, he won't wear it.

Outside of deleting the default outfit altogether (and having to pick up a naked NPC every time you dismiss him), are there any ways around this problem?

You could make a script to stash his outfit in a box, then give it back when he leaves your service.