If a country or private company authorized by their parent country set up a mine on the moon, who exactly could stop them? You can't blockade the moon, you can't evict them, and I doubt any country would really care enough to sanction the country of origin for the flight. The outer space treaty isn't worth the paper it is printed on.

It'll only become an issue when two competing countries/companies try to mine the same area of the moon. Until that happens, the question is completely academic.