I am Inuit (Inupiaq / Alaskan Inuit) and I strongly believe that there should be no American military presence in Greenland at all.
To start off with, their already existing base in Greenland both was created and is actively maintained via the violation of human rights. Thule Air Base was created by razing two Inughuit villages to the ground in 1953, Pituffik and Uummannaq. All of these residents were forcefully evicted and relocated, and the town of Qaanaaq was built where the families and their descendants now live. Uummannaq was returned to Danish control in 2003 but the Inughuit are still denied the right of return and are not allowed to use the area as traditional hunting grounds just as they did for hundreds of years before. Pituffik remains occupied by the US military. The former residents and their descendants in Qaanaaq want Thule Air Base to be dismantled and to be granted the right of return to Pituffik and Uummannaq for their traditional hunting grounds
Now, with the new upcoming base in Narsarsuaq and the new permanent American presence in Mestersvig, that is literally rewarding America for threatening to invade. When America first threatened to invade, the opposite should've happened, they should have kicked the American military out. If a country threatens to invade Greenland, their military should not be allowed in Greenland.
In addition, establishing a military base at Narsarsuaq directly threatens the safety of the residents. Just as Aki-Matilda Høegh-Dam pointed out how putting the Joint Arctic Command military headquarters directly inside Nuuk is a direct threat to the safety of Nuuk residents and effectively turns them into human shields, the same applies to Narsarsuaq. When you build a military base directly inside a civilian town, that will effectively turn the civilian population of that town into human shields (although Aki-Matilda has been weirdly silent so far on this when it comes to Narsarsuaq).
And even if you ignore all of this, it is necessary to acknowledge the immorality of partnering with the US military. The US is currently waging a murderous imperialist war against Iran, a war in which civilians are killed at a rate 7 times higher than the Russian invasion of Ukraine. Per HRANA, at least 1,721 of the 3,684 known deaths in Iran are civilians, making the civilian death rate around 47%. Now let's compare that to Ukraine. 16,126 civilians have been killed in Ukraine according to the UN, and BBC News estimated around 200,000 Ukrainian troops have been killed, making the civilian death rate around 7%. It is just as immoral to partner with the US military as it would be to partner with the Russian military.
And it's important to acknowledge that the US government doesn't actually care about the Inuit people at all, given how we Inuit are treated in the US where we have no self-determination and Alaska Native nations have been reduced to literal corporations. When they say they respect Greenlandic sovereignty, they only respect it because they're not allowed to violate it, not because they actually care about it.