"In this model, we assume that a large population of individuals comprises two distinct identity groups. These identities are assumed fixed, and thus correspond to a fixed feature of identity such as race, religious heritage, or socioeconomic background. Although such identities are fixed in the model, the salience of the identity, and therefore its impact on behavior, varies."
The model assumes only two distinct and unchangeable identity groups, and assumes that these identity groups are solely based on a few specific unchangeable traits. And that's before you get into some of the wacky assumptions in their actual math model.
Also of note, they mention Charlottesville and the capitol riot as examples of political polarization, but make no mention of comparable events on the left like the BLM riots, the GOP baseball shooting, etc. Gives you a good idea of where the politics of the authors sit and suggests there may be motivated reasoning behind their arguments. "Solve political polarization by doing more of what the left has wanted to do for over a century!"