Remember the game really pushes a nation to the point where it is today. Example modern day Babylon is Iraq. And the Iraqis most certainly use guns even today.
So Historically speaking the Mayan modernised counterparts evidently didn't use crossbows but stuck to their bows.

It may still be called a "Crossbowman" in-game, but you shouldn't worry about it much. It's Ethnic Units we are talking about here. Its job is to be Historical and in a way people can recognize a famous suit or vehicle of their respective country. England is famous for its Camel WW1 Fighter. Poland's most Notable WW1 Fighter was a License built German Albatross and so on.

Point is. Ethnic Units tries to be Historically Accurate, whether you like it or not. Personally I don't think its anything to moap about.