Nothing we do on the moon in the near term will require that it be to the exclusion of other countries. Landing a rover, or creating a moon base of a few hundred square meters still leaves a lot more moon for others.
Nothing except human nature ... see the current controversies in the South China Sea.
States are very territorial. There are emotional reasons for it, but also the exclusive claim for natural resources.
If water is found in mineable concentrations in only a few spots of the Moon, I bet there will be a serious conflict over those spots. It is literally a matter of survival for the future colonists.