Tribal Border Crossing Parity Act This bill provides the right to pass the borders of the United States (which confers the right to certain public benefits and other privileges pursuant to the Jay Treaty) to an American Indian born in the United States or Canada who is a member, or is eligible to be a member, of a federally recognized Indian tribe in the United States or Canada. Current law instead provides this right to an American Indian who was born in Canada and who has at least 50% American Indian blood.