For a great primary source for Christian missions and the Japanese Christian Church during early 20th century I can't recommend the Japan Christian Year-books enough. You can find many of them on archive.org. They are in English, but many of the articles in the later additions were contributed by prominent Japanese Christian leaders. The editions leading up to the Pacific War and those picking up after the war have a lot of content to dig into. There are of course plenty of monograms on the history of the church in Japan if you are near a decent research library.

I'll try to answer concisely. Christianity in Japan, at least in the modern era, has largely been an urban religion. Christian missions starting in the Meiji period largely focused on cities. By the late 19th century and early 20th century when Christian missions really began to pick up steam in Japan, many Christian denomination had a strong educational focus.

Protestant and Catholic missionaries alike started many colleges and universities during this period. Some of the leading colleges and universities in East Asia have Christian origins, as do many in the West. Many Japanese elite during the Meiji era sent their children to Christian schools. While very few Japanese people during this period became Christians, they largely came from educated urban backgrounds.

Nitobe Inazo for example became a Christian at University in Hokkaido and went on to become one of the leading intellectuals in Japan during the early 19th century. He was actually on the 5000 yen bill from 1984 until 2004. His book Bushido is really a must read.

The Christianity of this period was also highly politically active--one of my heros is a gentleman named Toyohiko Kagawa who was a labor activist during the early 19th century; his semi-autobiographical book 'A Grain of Wheat,' is a really fantastic read, even in English. Kagawa became a Christian as a young person, and despite having studied at Princeton in the US, he returned to Japan to work in the slums of Kobe. He was responsible for organizing labor unions, coops and even political parties--notably as one of the founders of the first Socialist political party in Japan. Kagawa was not the only politically active Christian in the early 20th century.

There are of course many other reasons for the large number of Christians involved in Japanese politics, but I feel that these are some of the major contributing factors. Christians have been more politically active in Japan than many of their peers, they tend to be well educated and because of their education are often in places of influence.

Follow up question: how did Japanese views of Christianity (and western religion as a whole) change during and immediately after WW2?

Follow up question: is their particular sect of Christianity related to any Dutch sects, being that they closed the island off from other European powers to stave off attempts at conversion? The Dutch said they wouldn't proselytize, but I can't imagine that it never happened.