  Magnetic topological insulators in the quantum anomalous Hall regime host
ballistic chiral edge channels. When proximitized by an $s$-wave
superconductor, these edge states offer the potential for realizing topological
superconductivity and Majorana bound states without the detrimental effect of
large externally-applied magnetic fields on superconductivity. Realizing
well-separated unpaired Majorana bound states requires magnetic topological
insulator ribbons with a width of the order of the transverse extent of the
edge state, however, which is expected to bring the required ribbon width down
to around 100 nm. In this regime, it is known to be extremely difficult to
retain the ballistic nature of chiral edge channels and realize a quantized
Hall conductance. In this paper, we study the impact of disorder in such
magnetic topological insulator nanoribbons and compare the fragility of
ballistic chiral edge channels with the stability of Majorana bound states when
the ribbon is covered by a superconducting film. We find that the Majorana
bound states exhibit greater robustness against disorder than the underlying
chiral edge channels.
