So says Preston Watamaniuk:
Does "galaxy at war" effect galactic readiness on all saves or just the current one that is being played? 
It impacts all saves. We found the other way was too confusing, and required a more complicated interface. 
His reasoning makes perfect sense. I will be extremely concerned however if this can't be turned off.
Unless whenever starting a SP game I can choose 'Ignore Galaxy at War Progress', I won't be touching MP at all. Would be terrible if I played my SP game, played MP and then replayed SP again, only to find I can't get my original ending again because the game was contaminated by GaW.