Naturally not every galactic member would react the same to genocide and bombardments. Some might not care, some might hate you for it. Hell there might be even some that will love you more for bombing someone else back to the stone age. Shows power and such.
But from a logic standpoint the civilizations that are against mass bombardments should be in the majority. Since there is always the fear they could be next.
Some don't seem to understand that it's not your civ necessary that objects to these actions, but rather the rest of the galactic community. Hence warmonger races might not care themselves to produce molten slagheaps, but the next door neighbor federation type wont be very amused.