To start with the most obvious one, it has been understood for more than a century that the Bill of Rights and the Fourteenth Amendment do not of their own force apply to Indian tribes. See Talton v. Mayes, 163 U. S. 376, 382-385 (1895); F. Cohen, Handbook of Federal Indian Law 664-665 (1982 ed.) ("Indian tribes are not states of the union within the meaning of the Constitution, and the constitutional limitations on states do not apply to tribes"). Although the Indian Civil Rights Act of 1968 (ICRA) makes a handful of analogous safeguards enforceable in tribal courts, 25 U. S. C. §1302, "the guarantees are not identical," Oliphant v. Suquamish Tribe, 435 U. S. 191, at 194, See also Cohen 667 ("Many significant constitutional limitations on federal and state governments are not included in the [ICRA]") and there is a "definite trend by tribal courts" toward the view that they "ha[ve] leeway in interpreting" the ICRA's due process and equal protection clauses and "need not follow the U. S. Supreme Court precedents `jot-for-jot,' " Newton, Tribal Court Praxis: One Year in the Life of Twenty Indian Tribal Courts, 22 Am. Indian L. Rev. 285, 344, n. 238 (1998). They have not surrendered their rights under the U.S. Constitution against the state or federal government, but only with respect to the Indian Governmental Entities of which they are a member.
The provisions of 25 USC § 1302 differ in language and in substance in many respects from those contained in the constitutional provisions on which they were modeled. The provisions of the Second and Third Amendments, in addition to those of the Seventh Amendment, were omitted entirely. The provision contained in § 1302 (8), differs from the constitutional Equal Protection Clause in that it guarantees "the equal protection of its [the tribe's] laws," rather than of "the laws." Moreover, § 1302 (7), which prohibits cruel or unusual punishments and excessive bails, sets an absolute limit of one year imprisonment and a $1,000 fine on penalties which a tribe may impose. Finally, while most of the guarantees of the Fifth Amendment were extended to tribal actions, it is interesting to note that § 1302 does not require tribal criminal prosecutions to be initiated by grand jury indictment, which was the requirement of the Fifth Amendment specifically at issue and found inapplicable to tribes in Talton v. Mayes, 163 U.S. 376, 16 S. Ct. 986, 41 L. Ed. 196 (1896). There is, for example, no right under the Act to appointed counsel for those unable to afford a lawyer. See 25 U.S.C. § 1302(6) which only provides that "and at his own expense to have the assistance of counsel for his defense"
Indians are fully covered by the U.S. Constitution from illegal acts by state and federal officials to the same extent as non-Indians. However, the U.S. Constitution is not applicable in tribal court. So Indians and non-Indians subject to tribal court jurisdiction have limited protections as extended to them by the Indian Civil Rights Act. It should also be noted that the only remedy the ICRA has for violations of it is a writ of habeas corpus. A writ of habeas corpus is a court decree that orders that a person being held in custody be brought before the court so it may determine the lawfulness of the detention. While an action under 42 USC 1983 for declaratory, damages and equitable relief may be brought against state officials for violations of the constitution.
This is why non-indians should not subject themselves to tribal court jurisdiction without fully comprehending what protections they do and do not have. However, this is true if you enter Canada or even Pennsylvania. Sometimes we as Americans think that because we are Americans we are entitled to the same "rights" where ever we are. However, those rights even vary state by state because some of the rights we enjoy are not provided by the U.S. Constitution, but from our State Constitution.