I'm pretty sure all the soldiers they interact with are WF but I agree it's hard to tell and I think that's the point. Although the president refers to them as secessionists and we only ever hear about three states in the rebellion I think it's easy enough to infer most of the nation was against the president since they did manage to overthrow him and the fighting wasn't just in the southwest. I don't think just California and Texas would be able to do that, especially with Florida dragging them down. So if the majority of the military joined the WF they would be the de facto military. Even though secession and rebellion are dirty words in real life I think the WF were supposed to be the good guys, taking down the corrupt government.
This map depicts the division of forces, including loyalist states:
https://gamefaqs.gamespot.com/a/forum/6/66655394.jpg
^The point the movie is trying to make is that there are other factors besides team color.