I believe that's the inevitable outcome.

The Chinese will build a moon base, as a sign from the Chinese government to the Chinese people that China is capable of cutting-edge engineering and science (notably a demonstration to their own citizens - when was the last time you heard about the Chinese space stations outside China?).

America seems a bit shaky in their determination to actually build a moon base, though having Jared Isaacman as administrator gives hope. But regardless of whether America is currently on track, a successful Chinese moon base won't stay without answer

The South Pole of the moon will end up one giant mega city due to it's constant sunlight. It will be a lot easier to get there once there is even one landing strip.

I will give you that. I will be more than happy to see both reach there in mutual success. I do fear the blow back of the more tribalistic folks that will see it as a threat rather than success.