One, I think Stephen Toulouse is only talking about swastikas because those are considered to have multiple meanings and there is a need to clarify that it violates the terms of use. There is no non-obscene meaning for a penis or animals having sex so there is no need to clarify that those will get you banned.
Two, while there are other equally tragic incidents in human history, the swastika is the only symbol that was used to directly represent the racism. Stalin was a horrible human being, but the hammer and sickle were never their to represent just him and his genocide, but was a symbol of communism and the Soviet Union. Similarly, while Andrew Jackson committed genocide against the Native Americans, the American flag is not representative of Andrew Jackson or his beliefs, it represents the United States. The swastika as a symbol for the Nazi Party is intrinsically connected to anti-semitism and the Holocaust.
Third, while I am entirely supportive of free speech and open discussion, Xbox Live is not the place for discussion. First of all, it is a private system, so your speech rights do not extend there. You do not have to be on Xbox Live, you do not have some natural rights to do whatever you want on Xbox Live. You have to play by Microsoft's rules. Don't like it? Go somewhere else. More importantly though, Xbox Live, as Toulouse points out, is inherently not capable of having historical and political discussion. It is there primarily as a gaming network. You are most likely not going to go there to discuss your opinion on the societal treatment towards the swastika. You are going to use Xbox Live to play slayer. As such, having a swastika as your emblem is not going to inform anyone of anything other than you support something that the swastika means, and like it or not, the most common answer to many in the world is the Nazi Party, who are a racist organization. As a side note, I am willing to bet the vast majority if not the entirety of people who had a swastika in their emblem before this announcement had it not because there is multiple meanings behind it, but because it is a quickly recognized symbol of racism and they were being immature and not really seeking discussion anyway.