The issue was apparently that one of the unit types SE creates was marked as an "enemy", meaning Begone! would destroy it, and that would mess up SE's assumptions about the game state. The easiest fix for now was to make it only delete units, unit spawners, and turrets. Hopefully that does not make this mod less functional in the environment of other mods. Guess we'll find that out eventually.
SE lists Begone! as an incompatibility, but hopefully they will adjust that now that the two mods put together no longer causes crashes. You can perhaps edit the SE info.json in the meantime and it will hopefully work.