To me it seems very strange that pacifist badge reduce war support of the enemy even when it is the pacifist who declared war. It is also possible to "farm" the pacifist badge as just asking for white peace when you are leading in war support give you the badge even if they refuse the white peace, which allow you to ask again for an additional level so you can reach level 3 in it without too much issue against certain opponents.

That does seem backwards.  If "War Support" is supposed to represent the will of the population to fight, it should reduce YOUR war support, not that of the person you are fighting.