...and if you have evidence that more people will quit your service because you allow swastikas than will quit your service because you don't allow swastikas, what would your duty be?

I feel a lot of complainers about political correctness miss this. Companies strive for political correctness not because of the personal sentiments of executives or investors, but because it makes them money to be PC. Allowing swastikas on xbox live would be making the service less appealing to customers in order to advance a personal ideal (that this is the internet and you should be able to say whatever the hell you want).