Skin handedness is set per install instead of per user

When selecting which hand a skin is, this setting carries over to all accounts that use the same install of Minecraft. However my two accounts have different handedness, meaning I must switch them every time I log into the opposite account. This should be easy to reproduce:
1. Start Minecraft with a main account.
2. Go into Options -> Skin Customization and change handedness to left.
3. Save and Quit.
4. Start Minecraft with a different account.
5. Notice this account is now left handed, even if it should be right handed.