Issue reproduced. Screenshot:

This is just a mild offset issue, this should be easily patched. Let me look at how exactly the rendering position is being derived.

I'm not sure what caused the issue in the first place, but modifying the offset from 1.62F to 1.68F fixed the problem for most of the cosmetic baubles. There are a few cosmetics which look like they've been broken for a while, so I'll sort through those later. In the mean while, the monocle and glasses now look right on other players:

The change is a single line in api/item/IBaubleRender.java, namely

            GL11.glTranslated(0, (player != Minecraft.getMinecraft().thePlayer ? 1.62F : 0F) - player.getDefaultEyeHeight() + (player.isSneaking() ? 0.0625 : 0), 0);

to

            GL11.glTranslated(0, (player != Minecraft.getMinecraft().thePlayer ? 1.68F : 0F) - player.getDefaultEyeHeight() + (player.isSneaking() ? 0.0625 : 0), 0);

Pull request forthcoming.