what was the justification for the use the cathode and anode terminology in IEF?
There is no redox taking place in IEF, just proteins interacting with an electric field
Who was responsible for this naming system and how can we change it?
Michael Faraday was responsible for the terms anode and cathode more than hundred years ago.
All the confusion regarding the nomenclature will vanish if you do not associate electrostatic signs with these two terms. One should identify the electrode labels with the redox processes rather than the signs.
These definitions are true whether you have a electrolytic or galvanic cell. This eliminates the need to call the negatively charged electrode as a cathode in an electrolytic cell or the positively charged electrode as the cathode in the galvanic cell. These definitions are self-consistent and hence nobody bothered to changed them.
Isoelectric focusing is "sort" of an an electrolytic "cell" hence its cathode is has a electrostatic negative sign because if we were to remove this gel and replace it with just salt water, we will see hydrogen evolution (= reduction of water) at this electrode.
The good mnemonic tool to remember is :
Anode = anabasis, electrons would be going upwards from the electrode to the wire = oxidation, ( Xenophon, Anabasis, 404BC, "The journey upwards(to north))
Cathode = cathabasis(the journey downwards), electrons would be going downwards from the wire to the electrode = reduction
That means a cathode/anode is the electrode where reduction/oxidation occurs, what means the flipped signs for a cell being a source/recipient of energy.
A cathode is:
And vice versa for an anode.
Anabasis/catabasis has application in other domains as well. E.g. ababatic/cathabatic processes in synoptical meteorology are processes related upward/downward convection of air,like at the front and the back side of the cold front of the 2nd kind.