It is my understanding that the telescope is a specific use structure. It may have living quarters for the people using it, but not for tourists. In the name of science and benefit for humanity, I am all for it. We need such telescopes to detect asteroids that may come in our direction.
Even so, you're taking a mountain with traditional significance to people in its natural state and building a big building on top of it.
Detecting threatening meteors is just an excuse. The telescope will be rented to wealthy tourists. They will not come in droves, because it will be an expensive, elite experience to visit and/or stay in the telescope, but it will exclude people from hiking up it and using it in the traditional, undeveloped state.