Those are all good points, but the sovereignty activists don't care. Each of them envisions themselves the new king or queen; this is about petty attempts at grabbing power, nothing more. They really don't care if they are wrong about the telescope as long as it gives them something to rally around (Hawai'i resident here; I have actually heard this said by an anti-TMT activist).
They don't want the economic or educational benefits the telescope would bring; poor and uneducated are good for the leaders. They want racial discontent more than then want tolerance; perceptions of persecution are good for the leaders. You can point out to these activist leaders out that Hawaiian sovereignty is an inherently racist idea (it's no better than the scumbag white nationalist groups, not in my book; all race based nationalism is immoral bronze age bullshit). You can point out that everyone born in Hawai'i is an American citizen equal under the law. You can point out the economic problems that would occur the instant Hawai'i left the US, if that were to happen, and that life for their supporters would become much harder. They do not care, and they don't care if Hawai'i goes to shit, as long as they are the rulers of shit mountain.
That's what this is really about. They want people poor, uneducated, angry, and easy to manipulate for their own benefit. None of the benefits the TMT would provide to Hawai'i County's public education system (like the high school robotics program they fund) and economy? That's great to them. They sure as hell don't want other people educating kids. And they do want people to say stupid shit like 'Hawaiians are anti-science' because it creates an us vs them environment (DO NOT SAY 'Hawaiians are anti-science' as some people have; that's racist and not true. Hawaiian does not equal anti-TMT activist). So we are not talking about a benevolent group here. Keep in mind, every year people do off road racing and snow boarding and other things on Maunakea, and leave all sorts of garbage, and no one cares about that. The Mauna is only sacred in so far as a political point can be made, in other words, they don't really give two shits about mountain or the telescope or the supposed sacredness, only what they can gain from it. Or course, if they really cared, they wouldn't be doing shit like introducing invasive ants.
Additionally, I'd like to point out that if they were really all about ancient Hawaiian traditions, they would realize that there was nothing prohibiting building things on Maunakea and that ancient Hawaiians were active stargazers. There is nothing at all suggesting that this would be offensive. The protestors also seem to be ignoring the fact that their presence on the Mauna would, in contrast, be offense; only the ali'i and kahuna were allowed on the Mauna, not commoners like them (of course, in the modern State of Hawai'i, we are all equals and Maunakea is open to all; there are no castes of people). It's no different than the Christian groups that make up their religion as they go along and pick and choose what parts of the Bible they like in order to justify their current inane actions. It's just like a lot of stuff that seems anti-science on the outside; it's all about someone's power or wealth, you just have to find out who, and in this case it is the Hawaiian sovereignty movement.
Hope that clear up some of the situation here. And the thing is, all of their legal, cultural, economic, scientific, and environmental arguments are complete fabricated bullshit. So whenever the telescope is built (because there is literally no good reason to block it) they are just going to use it as more 'proof' that they are being repressed, and that no one listens to or cares about Hawaiian voices (not true). The activists picked a target that gets them a win either way.