If your corporation is war decced by another player corp, and you decide to join a faction militia, will that war dec transfer over, making the aggressor corp a target for the faction navy and other militia members/corps?
After confirming with an ingame ISD, I can give you this answer:
Nothing changes. You will be at War with the enemy Militia and the opposing corp that declared war upon you will be only at War with you. The mechanics here are separated.