It depends on which Palestinian supporters you're talking about. I have found that there are those who might support the Palestinians in this particular conflict, but that doesn't mean their politics would align with each other on every issue.
However, there are probably more than a few who would probably be on the side of justice regarding the Native Americans. I had a co-worker from Sudan who was a devout Muslim and supported the Palestinians, but she was also extremely critical of US history, especially slavery, racism, and the horrific atrocities against Native Americans. Many Americans have also shared that view.
You spoke of some outside power (China or Russia) possibly supporting the Native Americans reclaiming their land. Interestingly, the US government once had similar concerns about civil rights leaders and organizations possibly being infiltrated or co-opted by communists acting at the behest of Russian agents. This caused some people to want to crack down even further on civil rights, while others believed that the better solution was to promote more civil rights and social justice. As a result, fewer people were swayed by communist agitators, as their situation appeared to be getting better through the current system, creating a disincentive to revolution or armed resistance.
So, if they want justice, then give them justice.