I was having the same problem with my singleplayer world and was able to fix it (at least it does not crash immediately, I have not spent much time playing to see if it will come back yet).
Make sure to make a backup of your world save beforehand in case something goes wrong.
Using NBTExplorer, I deleted all entries related to Hats as well as Morph in my playerdata file, as well as in the level.dat file.
To find these in the playerdata file:
For Hats:
ForgeData>Hats_hatInfo
ForgeData>PlayerPersisted>Hats_unlocked
ForgeData>PlayerPersisted>Hats_wornHat
For Morph:
ForgeData>PlayerPersisted>MorphSave
and for the level.dat file go to Data>Player and then follow the same paths above.
Note: This will delete all of the hats/morphs you have obtained in your world.
Hopefully this helps those with the same problem.
