As reported recently, China controls more than 51% of the hashing power and just in one province in China controls 54%.
This is technically incorrect: there is no way to measure what percent of hashpower is actually located in China, these reports simply look at what percent of hashpower is pointed at each mining pool (some of which are located in China).
With that in mind, if a government decided to 'crack down' on mining pools with >50% of hashpower operating within it's jurisdiction, then we would expect that the individual miners that contribute hashpower to that pool would point their hashpower to a different pool, which has not been compromised.
So to truly obtain 51% of hashpower, a government would need to compromise the actual ASIC hardware that comprises 51% of the network's hashrate. This is a much more difficult task, and it is unclear if a majority of ASIC hardware exists within one single jurisdiction, anyways. (remember, the location of a mining pool is not equivalent to the location of that pool's hashpower!)
To learn what an attacker with a majority of hashpower can do, see this question.
Note that Stratum V2 is a new mining pool protocol, which will lessen the power of mining pool administrators (and thus, the potential damage from a majority attack against the network). The following text is quoted from the Stratum V2 site:
Stratum V2 is the next generation protocol for pooled mining. [...] Stratum V2 introduces three new sub-protocols that allow miners to select their own transaction sets through a negotiation process with pools, improving decentralization.
From my understanding a 51% attack would just cause a loss of confidence, but wouldn't kill Bitcoin as the real chain will just fork off onto its own.
Proof of Work is how users decide what the 'real chain' is: there is no way to fork an attacking miner off the chain. Even if users all somehow collectively coordinate to fork the chain at some height (with the goal of avoiding the malicious miner's blocks), there is nothing stopping the malicious miner from just mining on the new fork as well.
A PoW change could stop the attack, but that is a very messy and complicated route to take (and if PoW is compromised for SHA256, it seems unlikely that some other algorithm would be more robust against the same attack in the future).