The TMT and its supporters did try, many times, to show how research in Astronomy could be considered a continuation of the traditions of Native Hawaiians, who navigated the Pacific astronomically (at least in part). Some Hawaiians agree with this argument. But there is a core group of Native Hawaiians for whom arguments about the merits of the TMT are irrelevant. They don't want more construction on Mauna Kea, full stop.
If something like this controversy involved a Native group on the US mainland, things might be simpler. There would probably be a native government for the Navaho, or Souix, etc that the TMT could negotiate with. If the TMT got the go ahead from the native government, then that government would deal with protestors among their own people, if the TMT did not get permission from the native government, then it would know that it could not proceed. But there is no widely recognized Native Hawaiian government. There's nobody for the TMT to negotiate with that all the protestors would obey. So the TMT negotiated with the state government, but many Native Hawaiians do not acknowledge the legitimacy of the state.