Note: My comment here is in my role as historian, not as development team.
When a present-day country is undergoing political problems, you have to ask if those are related to the depiction of history. Ethiopia's issues right now are - Menelik's name is invoked as an agent of domination and a villain. Burma's are not. I've been following Burmese events very closely (and was in the midst of taking Burmese language lessons in the morning before work when it all happened), but what this is about is a question primarily of the role of the military in politics and secondarily about the role of Burmese ethnic domination of the mountains.
The Burmese military had sought to stage itself as the power behind a nominally democratic state (as Thailand is now), and when it looked like, no, they had signed up for an actual democratic state, they stepped in with catastrophic results. But I have not heard the names of Pagan, or Ava, or Toungoo invoked by the military, so for a historical game I don't see a conflict. Burmese warfare against ethnic minorities does indeed have a historical dimension, but, again, the focus of ire in this fight are 20th century military leaders and not historical rulers. While myself as an anthropologist and a specialist of Southeast Asia I am closely following the situation, I don't see flags coming up over a historical representation of a Burmese power in a game like Civ. Not yet, at least. The worst thing that we would want would be to be seen to endorse a particular reading of history (though, of course, there is no objective stance outside of history), especially one on the side of violence.
Again, this statement is entirely one made by Andrew Johnson, the scholar, and not Andrew Johnson, the writer for Firaxis.