One thing I'm unclear about is this: "If Congress wishes to withdraw its promises, it must say so." The question in the case, as I understand it, was whether previous acts of Congress had in fact dissolved the reservation. Could Congress, if they wanted to, pass a resolution saying, "Actually, such-and-such bill from 100-some years ago dissolved the reservation." Or can they only say, "Starting today, the reservation…
As I understand it: The court's job is to interpret the law under specific circumstances.
As a stupid example, lets say that congress makes a law that you can't have those fake flamingos on your lawn, else you'll go to jail. Fred ignores the law and puts some fake flamingos on their lawn. The executive branch enforces the laws, so the police arrest Fred. The courts rule that you violated the law, so to jail you go.
Bob is rebellious, so he paints his fake flamingos with orange spray paint. The police arrest Bob under that law, and in court he argues a core characteristic of Flamingos is that they're pink. So really he just has decorative orange birds in his lawn. If the court agrees with his argument, then he goes free. This sets a precedent: The judicial branch didn't really make any laws here, but they kind of did. Courts don't have the power to make laws and decide on a case by case basis what's legal or not. So they take breaking precedent as a really, really big deal.
Now what congress can do is go back and make any birds in the form of flamingos illegal, no matter the color. Now that the law has changed, the courts will use a new interpretation, and Bob could now be arrested if he doesn't take down his "decorative orange birds".
However, he could make another argument in court: That he has the first amendment right to have orange flamingos because that's freedom of speech. The courts (possibly up to the supreme court) can rule that he is indeed protected by the first amendment, and nullify congress's law.
Of course, the constitution can be amended. So if people really hated fake lawn flamingos, they could go through that process and remove the first amendment's protection in this case. The bar for changing the constition is so high that it basically doesn't happen for anything political.
This is why the supreme court's rulings can be so politicized, against the court's wishes. The courts aren't political because they don't make laws, and are intended to be impartial interpreters of it. However a 5-4 split supreme court ruling today is basically law until there's a super-super-majority of people who want to change it.