While investigating why I was unable to load_session when I had some ufuncs from scipy.special, I noticed that dill fails to determine the module the function belongs to depending on the order of the imports:

On a fresh interpreter session (Python 3.8.6), if you load dill prior to loading scipy.special, you get:

>>> import dill
>>> from scipy.special import gdtrix
>>> dill.dumps(gdtrix)
b'\x80\x04\x95\x1a\x00\x00\x00\x00\x00\x00\x00\x8c\x0b__mp_main__\x94\x8c\x06gdtrix\x94\x93\x94.'

Notice the incorrect __mp_main__.

Now, if you invert the ordering of the imports:

>>> from scipy.special import gdtrix
>>> import dill
>>> dill.dumps(gdtrix)
b'\x80\x04\x95$\x00\x00\x00\x00\x00\x00\x00\x8c\x15scipy.special._ufuncs\x94\x8c\x06gdtrix\x94\x93\x94.'

Oddly enough, if we call pickle.whichmodule, it finds the correct module irrespective of import order:

>>> import pickle
>>> from scipy.special import gdtrix
>>> pickle.whichmodule(gdtrix, gdtrix.__name__)
'scipy.special._ufuncs'

Or:

>>> from scipy.special import gdtrix
>>> import pickle
>>> pickle.whichmodule(gdtrix, gdtrix.__name__)
'scipy.special._ufuncs'

The only way I can think of getting an incorrect module is to pass name=None to whichmodule:

>>> pickle.whichmodule(gdtrix, None)
'__main__'

Which might indicate that some cache is initialized when the module is loaded and it somehow fails to update for some types?