I was wondering, did any Native American tribes ally themselves with one side to attempt to overthrow the other? Were they treated equally bad by "both sides" (North & South) so they just stayed out of it? Did they attempt to destabilize the US government(s) and attemp to retake land? Did they engage in politics?
This is such a fascinating question, since settlers controlled only about half of what the USA is now back in 1860; what exactly were all those other people doing?
Some disregarded it as it didn't effect them, such as the powerful polities in the North Pacific coast who had little contact with settlers. Others disregarded it as they were de-facto at war with all settlers, such as the Dine' (Navajo) and Mashgale-inday (Mescalero Apache). But many were caught up in the fervor, picking a side and raising regiments.
Not everyone picked the same side though, and the situation in Oklahoma was the most fraught. Of the "Five Civilized Tribes," those who had been slavers and built Euro plantations such as the Tsalagi (Cherokee), Chahta (Choctaw), and Chikasa (Chickasaw) supported the Confederacy; while on the other side, those who had significant African intermarriage and were anti-slavery such as the Mvskoke (Creek), Simano-li (Seminole) supported the Union. This led to immediate conflict...
I'm not a specialist in this period but here are a few answers to this question:
Also if you were curious as to what was happening in Virginia, here's a great lecture about the Pamunkey's role in the Civil War (pro-Union) by Pamunkey PhD Ashley Atkins Spivey: Union Tooth and Nail: The Pamunkey Indian Tribe and The Civil War in Virginia