I had a similar problem with my 1996 175xl. It seemed that the radio would power on sometimes. But i have a battery switch (dial with BAT1, BAT2, BOTH, OFF) in the Engine Compartment. Now when I am done with the boat I just switch it to OFF. I dont know if you have the same type of batter switch back there under the engine cover by the batteries and engine.
With these used boats its sometimes all about the what the guy did before you. Also, your boat is newer then mine so not sure...there are a lot of good guys here on this forum who may be better help.
PS I did have the boat mechanic put a new ignition key switch in that had an "accessory only" setting when key was turned left. left is accessory, middle nothing, right engine start and run.