Your character is simply mirrored when you face into the other direction.
It'd certainly be possible to redraw skins for the other direction and reposition equipment (so that earrings only show up facing one direction, for example). However it'd simply increase memory requirements and general complexity, without much benefit.
So, not a bug, but a deliberate design choice that has the disadvantage you mentioned.
Yup, repost, but my previous answer completely answered the bug you reported.
Anyway, I'll be closing this thread, since it's not really a bug, but a design decision that will not be changed.