"We both have the same charge, Batman -- and like charges repel each other!"
That adds an interesting twist. c x c --> mutual repulsion, but c --> unilateral repulsion (i.e., zebra-Batman and Zebra-man are mutually repulsive, but zebra-Batman repels normal-objects without being repelled himself). This is suspiciously like a flux of particles obeying Fermi-Dirac statistics. Particles obeying F-D stats take up space because they have a maximum density; if they carry some sort of charge, they would also run away from each other; if they couple weakly with one or more particles in the Standard Model of Quantum Mechanics, a large "sandpile" of these hypothetical particles would disassemble (thermodynamics), transferring some of their momentum to ordinary standard model particles which would be accelerated in largely the same direction.
We can compare this to a neutrino. Neutrinos are fermions, so obey Fermi-Dirac statistics. They have no electric or magnetic charge (thus "neutr"ino). They interact only very weakly with some other standard model particles; their interaction cross-section is very small. They have small rest mass, so they accelerate to relativistic speeds given tiny accelerations i.e. they move very close to the speed of light all the time. There a lot of neutrinos zipping around from all directions (almost uniformly: there's more from the direction of our closest big nuclear fusion reactor, aka our Sun). We can observe them occasionally knocking the hell out of atomic nuclei, either breaking them up or imparting large accelerations to them.
If the "zebra force" was just a huge flux of neutrinos as we understand them, things around zebra-Batman would be extremely radioactive due to weak force interactions (nuclear decay); we need something like a "thermal" neutrino analogous to thermal neutrons. "Hot"/"relativistic" neutrons are produced in some nuclear decays, like Uranium-235; these can have their kinetic energy reduced by a moderator (graphite, water) to become "thermal" neutrons, which more readily interact with nearby U-235 nuclei, causing them to decay). Thermal neutrinos are not totally alien to real-world physics; they are expected by some hypotheses based on the standard cosmology.
A particle like a thermal neutrino that imparts momentum to an atomic nucleus without breaking the nucleus apart would, given a large flux emitting from a point (or the surface of zebra-Batman) probably carry normal matter away much like as depicted in the comic panels. Two sources of such particles, when brought together, causes problems with the maximum density of fermions (the Pauli exclusion principle), and so zebra-Batman and Zebra-Man being forced apart as shown is not a surprising observation.
There are still serious conservation of energy and momentum problems for our emitters, though, and I'm sure you're all bored to death of this by now. :-)
It's hard work to make sense out of comic book physics. It might seem strange, but Silver Age Crack is often easier to cope with than today's comics, in large part because the apparent energy of the "mysterious powers" (or advanced technologies) used in modern comics is often higher.