Centralized China has been using about the same measurements for at least 500 years. Hundreds of millions of people using a system of measurements and then suddenly at 1925, the government decided to ditch the old system and use metric. Now at the Wikipedia article for Metrification, China's status as a Metric country is at "almost entirely complete". How did this happen?
The 1920s and 1930s saw major advances in government policy regarding standardisation. The relevant organs were highly motivated as it was felt that this was the only way to be a modern nation and be in line with the advances that science was making at the time.
Relevant to my personal area of work. this was also the time that the state introduced a standard lexicon of scientific terminology. Before that, different people in different parts of the country were using different terms of the same thing. In the hard sciences this was seen as a major hinderance to progress, and so the government released the standard list so that everyone would be on the same page.
Likewise with units of measurements, the common units such as 斤、尺 etc were changing from dynasty to dynasty, ruler to ruler (pun intended). The 尺-length measuring sticks that I have are all from the last 100 years and so are pretty consistent, but it wouldn't be uncommon to have major variances. One 斤 in China is now 500g, but in Taiwan and Japan it's 600g. Hong Kong, Macau, Singapore are 604.8g, but then in Vietnam it's 604.6g just to make things more confusing. One of my hobbies is classical architecture like you'd find in the various versions of 《營造法式》, and it's always a hassle to sort out what measurements the labels are actually referring to.
The 1920s was the Post-May Fourth world. Scientific progress was of paramount importance as a way to save China from foreign imperialism, and that meant playing some serious catchup to the perceived level of scientific technology of the time. Standardising measurements to the international standards was a huge part of that, as was standardising the way these things were discussed. There was huge motivation, and there was a desire to make it happen in groups like the Ministry of Education who were the people you'd really need on board to effect this kind of large scale change.
Then, with the Communist Party taking over in 1949, much of what the Nationalist government had begun was continued, especially in terms of educational reforms, so it was able to continue quite easily.
tl;dr: The State saw the value in the change and so made sure it happened.