There are people who consider Mauna Kea to be sacred and there's not really anything that could argue against a specific person's particular belief.
However I will say that there is no widespread religious activity involving the top of the mountain. There are far more people performing ceremonies and leaving sacrifices at Kilauea or even just various heiau, a type of man-made temple site. Even that is a very low proportion of native Hawaiians.
People feel respectful of it and it has widespread meaning but these feelings are barely above average compared to the respect felt for all other geographical regions and features of Hawaii.
My point here is that there's no substantive disruption to anyone's religious expression.
Even these religious activities are pretty rare, as Christianity was pushed pretty hard once missionaries converted the royalty in the 19th century.
Most of the time when people are against building telescopes, the conversation seems to carry on to reveal that it's kind of a proxy used to air greivances for the long history of ethno-political issues.
There was a reference above referring to the telescopes as a violation of the Kingdom of Hawaii which hasn't existed for over a century- to include a telescope under that standard you would literally require the formation of a new country. Obviously in that case, building a dog house by the ocean would be equally impermissible.
Ancient Hawaiians took their religion very very seriously, and still had quarries up there due to high quality stone availability, so they didn't seem to think technological exploitation was much of an affront.
From what I know about Uluru, it's far more significant to a much larger swath of people, and it's a much smaller area than a whole mountain.
Someone could have a different perspective than I do or might know something that would invalidate some of the points I made, and I welcome the input.