If they're natural born into this country and out of their Indian nation, there is no "pledging" involved.
See Elk v. Wilkins, 112 U.S. 94 (1884) for a little bit. I don't know much about the details of citizenship of Indians in the US, nor do I recall much about the Elk case, but the syllabus opens with "An Indian, born a member of one of the Indian tribes within the United States," and this Indian was not a NBC of the US, that's for darn sure.
Indians not taxed were specifically excluded as far as I know from my reading.
You are correct...my bad...my confusion was caused by the 14th amendment language. When I investigated it over another matter, I now recall that the jurisdictional language was meant to exclude Indian nations for citizenship.
At the time I was studying it from the standpoint of freed slaves. Got them confused..”Subject to the jurisdiction thereof”.