How is it not a problem if a repressive government gets ahead of the west in R&D? Do you like more, or less repressive government and the wrongful imprisonment of dissenters?
You speak of China as if they were the same as North Korea, or worse, which is manifestly untrue. China, in the 60es, was repressive, no doubt, and you could see it in the fall in living standards, but things have turned around in a radical way since then. Have you ever been to China? If you ask anybody whether they think their government is repressive, they will tell you that the government does what it should - that it does what the people wants. As an American you may not like it, but since this is not your country, your opinion doesn't really count. As for China getting ahead of the US: up your game, invest more in proper education. The US is still a bit ahead, but for how long? You are letting it slip through your fingers, playing with silly superstitions.
Again, would you like a militarily aggressive force controlling the moon?
Isn't that more of an argument against the US being present there? Or European nations? Or Russia? In fact, of all the superpowers, China seems to have conducted the fewest wars of aggression in the last few centuries. The West has always had its excuses ready - civilising the savages, rolling back Communism etc, but excuses is all they were. As for controlling the moon - how do you imagine they would do that? Send 100 million Chinese up there to occupy the whole surface? Planting a flag and going "Mine! It's mine I tell you! Mwahahaha!!!"? Even establishing a base similar to one of the Antarctic research stations is going to take decades, no doubt. It will be centuries before any talk of dominating the Moon is remotely relevant.