Question: Is this just a "Hawaiian" thing? Does stopping the TMT only benefit Hawaiians, at the expense of everyone else?
Answer: Mauna Kea is very sacred in Hawaiian tradition. Hawaiians have been caring for the mountain, and conducting ceremonies and burials there, for thousands of years. In addition, Mauna Kea is sacred to people from all around the world. Protection of sacred places is something that is a part of all human cultures. And because these sacred places are often very special in terms of natural resources, their protection really does benefit everyone.
The indigenous peoples of the world are sometimes referred to as the "canary in the coal mine" of humanity. This comes from the days when miners would carry canaries into mines in order to warn them of dangerous conditions, such as invisible poisonous gasses in the mines. If the canary became sick, the miners knew that they would soon become sick, too. In the same way, problems that seem to affect only those from the indigenous culture of any given place will probably also hurt the society as a whole, if continued. Protecting indigenous cultures is therefore a good way to ensure that all of humanity will stay healthy for generations to come.