Here is the unpublished opinion in Chavez v. Navajo Nation Tribal Courts.
An excerpt:
The district court dismissed the case for lack of jurisdiction. The court held that Mr. Chavez’s lawsuit against the Tribal officials could not be maintained in federal court under §1983 because all of his challenges to the Tribal officials’ actions relied on Tribal law. See Burrell v. Armijo, 456 F.3d 1159, 1174 (10th Cir. 2006) (“A § 1983 action is unavailable for persons alleging deprivation of constitutional rights under color of tribal law, as opposed to state law.” (internal quotation marks omitted)); see also Polk Cnty. v. Dodson, 454 U.S. 312, 315 (1981) (observing that acting under color of state law is “a jurisdictional requisite for a § 1983 action”). Turning to the Tribe, the court held–after noting that Mr. Chavez failed to even address the Navajo Nation’s sovereignty–that Congress had not authorized suit “against tribal entities pursuant to 42 U.S.C. § 1983.” R. at 631. See Nanomantube v. Kickapoo Tribe in Kan., 631 F.3d 1150, 1152 (10th Cir. 2011) (“[A]n Indian tribe is not subject to suit in a federal or state court unless the tribe’s sovereign immunity has been either abrogated by Congress or waived by the tribe.”); E.F.W. v. St. Stephen’s Indian High Sch., 264 F.3d 1297, 1302-03 (10th Cir. 2001) (observing that tribal sovereign immunity “is a matter of subject matter jurisdiction”).
Mr. Chavez appeals.
Briefs and lower court materials are here.
Turtle Talk 
This seems like a sovereignty win, but I wonder, after Plains Commerce Bank’s discussion on 1983 actions, whether all this separation of the federal constitution and system from tribal institutions is starting down a path toward outright isolation for tribes, total self-reliance, decreasingly worse logic and norm guiding the federal/tribe and state/tribe relationships. On the flipside, while we all the US Const doesn’t apply to tribes, it seems a second means of applying it has become entrenched (the first was the SCOTUS simply declaring tribes lack jurisdiction): certain tribal actions and matters, usually through some tribal constitution action requiring Secretarial approval, increasingly find themselves in the IBIA, where the analysis is based on civil liberties and civil rights, usually in the form of ‘due process’ or equal protection, even if the admin opinions never use the words. Think tribal elections or actions athat affect member property, especially the “allottee member” canard.