No doubt being too PC is bad, esp. when it results in choices that are less fun. But going to far the other way (ONLY cultures that had a major impact on europe) is just as silly.
The Aztecs had a large and long lasting empire, just because they got defeated (by more than a handful, and by vastly superior technology and disease), and are now homogenized into other cultures (mexico, mainly), doesn't mean they are not a worthwhile civ to fit. I think the Aztecs are a great choice for civ, they had a large empire, distinct culture, and they have a nice geographical location for the world map. The mongols don't have squat now either, doesn't mean I wouldn't want them included.
As for the "Arabs", for someone flinging around history so much you should be more careful. The Ottoman Turks (who I guess are who you mean by "Arabs") were much further from fanatical than, say, Europe was, even after they got smacked around by the crusades. They were much more interested in making money via trade. The fanatacism you are referring to is a VERY recent development (last 60 years or so) in the Arab world on a political level.
I'm as opposed to needless PC as the next guy, but when being anti-PC is the same as just being plain ignorant of other cultures, or having some Euro tunnel-vision of history (like all the history textbooks did before multiculturalism entered the discussion), is worse.