I can't see how this would be offensive because, generally, a gamertag applies only to the person in question so if someone wishes to call themselves "MoneyCrazedJew", people are just going to assume that is what he [believes he] is.
If a stink is raised, how much are you betting that all the complaining will be done by people who are neither jewish or even know anyone who is jewish and that that the majority of jews couldn't give a flying fuck?
If it was something less personal or something worded so that it applies to others then a shit-storm might be more warranted. Something like "NaziSympathiser" or "GodHatesFags" for example. Merely adding an "s" to his gamertag making it "MoneyCrazedJews" might start pushing the boundaries too because it now refers to jews in general rather than an individual.
In the end, if he wants to call himself "MoneyCrazedJew", even though he isn't, fine. I call myself "MajorWard" although the closest I ever got to achieving rank was being a Leading Cadet in the ATC. No-one from the armed forces has complained...
It's not worth getting into a flap over.
Wardy