Historical significance and geographical diversity are probably the most important factors, but I suppose popular interest is also taken into account. Also, I believe not only global significance is taken into account, but regional significance, but I'll explain this later.
I mean a hypothetical set of nations for Civ V that never became even regionally powerful, chosen because the developers wanted them to get another go at becoming a superpower. Basically it's just a joke, feel free to ignore it.
But isn't everything in Civ based on influence? While Civ IV's civ set was quite inflated (having relatively minor and even unexistent empires), all the civs had accomplished something that made them regionally or globally influental.
Ok.
Yeah, obviously the one thing that they seek is to make an enjoyable game, but I don't think superpowers and minor civs mix well, especially when there's this new city state system specifically for less dominant nations.
Obviously they have other criteria as well. But historical significance plays large enough role to make it feel very odd to have a minor nation like my beloved Finland fighting the USA, Russia and China. By the way, I also find conflicts through time quite weird too, especially between nations that occupied the same territory (like Holy Roman Empire and Germany).
I mean overall global or regional influence - financial power, resources, population, wonders, military power, technology, culture... everything that makes a civ stand out. Jews certainly have some of these: they are, after all, one of the oldest surviving cultures and many of our moral standards are based on theirs.
However, all Civs in Civ IV were called empires, because that's what they were. They were able to make their neighbours bend to their will, often by arms, sometimes by trade. Jewish people didn't stand out in this field. They could never become powerful enough to manipulate their neighbours or bash their heads in. They lost control of their land ages ago, and now have controversially reclaimed it by force. It's not an unified or stable empire, although I hope for the sake of everybody involved in that conflict that a peaceful solution is found as soon as possible.
Read my original claim again and observe that I pointed out that the selection is possibly biased to provide diversity.
About Aztecs, you're right. Aztecs controlled a region smaller than modern Mexico. However, Aztecs were quite sophisticated and rich, and were able to enslave many neighbouring peoples. They were regionally very powerful and the most advanced empire in the area, and this is probably why it has been in Civ since Civ I if I recall correctly. Their culture is also very different, so they could also be in to provide diversity.
However, Aztecs were easily wiped out by the Spanish. It was by no means an even fight. Aztecs lacked a fundamental aspect of a Civ-civ - technology. They built fancy temples, but were a lot more primitive than other (surviving) Civs-civs at that era - perhaps they were (in Civ terms) more like advanced barbarians than a primitive civ. I'll leave that up to the developers, but I have to say that the city state system would fit the Aztecs like a glove, just as with Israel.
(Of course I could do that myself)