> the Moon belongs to no people yet, versus the opposing view established by the Outer Space Treaty that the Moon belongs to all people

You're describing the Moon Treaty, which was never ratified [1]. It would have made the Moon the common heritage of all manking [2]. The Outer Space Treaty is far less restrictive [3].

And even if the Moon Treaty were in effect, it still wouldn't make lunar colonisation an assertion of human privilege. It would be an assertion of certain humans' privileges over others. But there is no non-human concern in play to any practical effect.

[1] https://en.wikipedia.org/wiki/Moon_Treaty#Provisions

[2] https://en.wikipedia.org/wiki/Common_heritage_of_humanity

[3] https://en.wikipedia.org/wiki/Outer_Space_Treaty#Provisions