My own personal take on the propaganda is that it depends on who is meant by “rats”, etc. The purpose of the Just War Doctrine is to minimize the damage and deaths due to the prosecution of the war. I would take the sign as an encouragement to the defense worker that his efforts are making a difference in winning the war. I don’t think it is an encouragement to mistreat the enemy.
On a different note, a just war must have a reasonable chance of success. Is it possible for a just war to evolve into an unjust one by gradually putting extraordinary restraints on its troops in the combat zones to the point where there is no longer a reasonable chance of success?