What could China and Russia do on the moon that would alarm the US along with other countries?

They could violate international treaties limiting the weaponization of space.

Remove the US flags.

They could lay claim to and begin extraction of valuable metals, minerals and water ahead of us.

Build missile bases.

You have no details, so I don’t know if you are thinking of space force, or just the moon only.
The moon is known to have benefits we did not know for a long time. There could me yet more.

Space Force, the Guardians, are not about the moon, much. It is not about little green men. It is about patrolling the satellites to make sure none of them get weaponized. Also, if another country beat us to it, we would be thumbs up our arses.