The idea was pretty strong in Hungary and Japan during the interwar period and WWII. Check out
the contemporary Hungarian website for additional info.
The Turanian National Alliance was founded in Japan in 1921 and the Japanese Turanian Society in the early 1930s. On the other hand, there used to be such ones as Turanian Society (1910) and Turanian Alliance of Hungary (around 1920) in Hungary.
"Japanese language belongs to Turanian (Ural-Altaic) ones. (Turanian is to Ural-Altaic as Aryan is to Indo-European). Though the word "Turanian" originaly means one of the families of language, it has also started to be used as a racial term especially in Hungary and Japan during the 1920-30's with the racial term "Turanid". Turanian Identity of those days was based on the theory that Turanian peoples had some cultural or racial relationships.
According to Turanism, that is the reason why Japanese language has grammatically something in common with Hungarian one. Hungarian and Japanese Turanists maintained that the forefathers of the Japanese had originated in the Euro-Asian region and ressetled in the main island of Japan.
In Japan, there used to be such Turanist organisations as "Turan Minzoku Domei" (Alliance of Turanian People, 1921), "Nippon Turan Kyokai" (Turanian Society of Japan, early 1930's), and Nikko Bunka Kyokai (Japanese-Hungarian Cultural Association, 1938).
Anyway, the characteristics of Turanians is in that they perceive their native languages in their right brain. Most of the languages in the world are perceived in the left brain. However, Japanese language is so peculiar that Japanese people perceive it in their right brain. Turanism is a part of Eurasianism.
Those events could only be the end part of a long chain events, which I doubt would lead to the same result each time. There are so many independent parameters involved.
Not any more. No such law exist anymore.