So says Preston Watamaniuk:

Does "galaxy at war" effect galactic readiness on all saves or just the current one that is being played? [1]

It impacts all saves. We found the other way was too confusing, and required a more complicated interface. [2]

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.