A shopkeeper who hates you (e.g. for having stolen from them) will be reluctant to serve you and will insist you wear a shirt and shoes before you enter.

In variants with racial shopkeepers, the shopkeeper can also hate you on principle without you doing anything wrong. In variants with Convicts, their striped shirt could be unacceptable for purposes of having a shirt.

A headless race, “Akephalos/oi”, which has no head and its face on its chest, so it is incapable of wearing helms, and is blinded (and cannot drink potions) if a shirt or body armor is worn.

Also a dullahan/cephalophore race which Knights can play as. They are also headless and cannot wear helms, but they carry their head as an item and can place/throw it elsewhere. Vision is based on where the head is, so it is possible to leave the head somewhere and have the body moving around blindly in a different area of the map.

Woolen shirt, shirt-slot armor which gives zero AC but cold resistance.