It can't be in each other's gravity, else the same phenomenon would affect dark matter. For something to affect regular matter but not dark matter, it has to be an electromagnetic interaction (at this scale - as the weak and strong forces only interact on very very small distances). So it has to be a significant amount of head-on collisions, or some kind of charged dust clouds projecting large EM fields.

I interpreted that as gravity causing things from the two galaxies to mix up, after which normal matter can interact electromagnetically (in more head on collisions than usual) but dark matter won't.