In order to answer this question, we have to think of Junior within his own cultural context. As a Native American, Junior is surrounded by many different cultural phenomena for which the "white man" is in large part to blame. In his own family, he has experienced crippling alcoholism, death, and diminished opportunity for success. He is very aware of the challenges that he faces specifically because he is Native American. He even witnesses his best friend, Rowdy, being beaten by his own father, and takes part in a few fights himself. Violence, addiction, and death are a very large part of the world that he lives in, but he is also very proud of his heritage and recognizes the many beautiful things that fill his life: the warm smell of fry bread, his grandmother and her old school ways, and the pow-wows that he sometimes attends. The Rez is also very beautiful and home to many colorful characters who are important to him, and whom he would defend against outsiders, because when you're an oppressed person like Junior is, you realize that you need to stick with the people who defend and support you.
Having said that, I think it's safe to say that Junior would feel weary of outsiders at the very least, and even more likely is that he would outright not trust them. There is an understanding among Native Americans who live on reservations that you just don't really trust a white person, because you can't, given the history. And on Junior's reservation, it's no different. When the white millionaire comes, lugging the heavy beaded dance outfit that he believes belonged to Junior's grandmother, everyone looked at him with awe first, before they realized that he was full of it. Still, they didn't like being scrutinized and examined for their culture. They felt like this guy was treating them like a novelty and he was, essentially, though he didn't see it that way.
So even though everyone was respectful enough to hear him out, they felt uncomfortable and disliked him being there. They were even confused about the old white hippies who liked to hang out on the reservation. Junior realizes, as they all do, that there is a cognitive dissonance that goes along with ignoring their oppression, but pretending to appreciate their culture. When you can ignore the many ills that befall Native Americans, but use your knowledge of their culture as a status symbol, or come to "hang out" with them because they are a novelty, you become a person that Junior simply cannot trust. It follows that he would treat someone like that with a healthy dose of skepticism.