Speed alone is not dangerous: airplanes travel much faster than 375mph. What matters is how the proposed trains are made safe for passengers. Most cases of train crashes are due to human error or outdated technology. The Japanese bullet train is an example of a very fast but very safe form of transport. If the Chinese follow the Japanese example, all should be well.
Yes, it is my belief that China's new train will be safe for passengers to travel on. This is because we know that it is relatively safe to fly on airplanes that reach 500-600 miles an hour, so traveling at about 375 mph is a lot slower and since trains are closer to the ground, these trains have to opportunity to be a lot safer.
Yes, it is safe to travel on a vehicle that would reach 600 kilometers per hour because airplanes travel much faster. There is no reason for it to not be safe. Since passengers are inside the vehicle, we will move as quickly as it can go. It is not like it will leave us behind.
I think that travel, even at high speeds, can be very safe providing it is engineered well, maintained well and the routes are well organized. Actually, I would suspect that speed has little to do with the overall safety of transportation, and rather, minimizing human intervention, and thus human error, has a much larger impact on safety.