You would rapidly but temporarily lose your 'friendly' (or otherwise) friendship status, NOT the rank or even reputation you've gained. However, this might affect your gameplay if you are still trying to rank up with the federation, as it will take a long time to get back to allied again and that will have a strong effect on the rep you gain from other activities (the higher your friendship status is, the faster you gain 'rep' both with the superpower and minor factions allied to them). Incidentally and simply for the sake of completeness, it's worth mentioning that friendship status with a superpower both decays when high, and increases when low, in the absence of any interaction affecting its direction,until it takes the middle of the bar where it stays.
You will also become hostile with the fed faction you are fighting due to this new loss of rep from conflict zones, and after a certain number of czs your support will become more and more inconvenient, until you are forced to hand in and rearm after each cz at the nearest interstellar factors.