No they cannot do business with Chinese governments, ITAR forbids this.

There is already history here where a failed Chinese rocket crashed with a classified American payload and caused the whole satellite anything is now ITAR

I wasn't thinking of OFAC, I was thinking of this: https://en.m.wikipedia.org/wiki/China_exclusion_policy_of_NA...

If NASA is forbidden from working with organizations affiliated with China, it seems to me that SpaceX working with China might imperil their collaboration with NASA. Then again maybe not, I don't know the answer.

Answer is no. SpaceX is not NASA.

I know SpaceX is not NASA, that's not a valuable insight.

Edit: It seems the situation is not nearly as clear as you believe: https://www.satellitetoday.com/government-military/2020/08/2...

Considering a less direct relationship with China already has some congressmen evidently perturbed, I think there is a decent chance SpaceX would refuse any contracts with China if for no other reason than to avoid provoking Congress further.

Ok so the answer you want is yes. Congress people can say whatever they want for political reasons, and because SpaceX is vastly out performing their preferred old space contractors, they are motivated to attack SpaceX for the smallest most ludicrous reasons like this.

But they also aren’t likely to pass any specific legislation or change what Elon does.