What about an established state converting to Judaism? My proposal would be North Korea.
The Kims adopted quite a lot of ideological influence from Imperial Japan, which was actually quite pro-Zionist and went out of its way to promote Jewish settlement in the hopes that American Jews would influence US foreign policy to be more pro-Japanese, and in the hopes of attracting Jewish capital for industrial development. Japan also was very interested in Zionist cooperative agricultural settlement and saw it as a model for Japan to emulate.
North Korea's Juche ideology is also seen as kind of a syncretic religion combining elements of Marxism-Leninism and principles drawn from the pre-existing religions in northern Korea, which now are primarily neo-Confucianism and Korean shamanism. However, before the Korean war, North Korea was actually quite heavily Christian, with Christianity having historically had a strong link to Korean nationalism. And, so, one of the first things that North Korea tried to do ideologically was establish a pro-Communist "Christianity with Korean characteristics" in the form of the Korean Christian Federation, headed by Kang Ryang-uk, a close advisor of Kim Il-sung. (The Korean War shook this up somewhat, what with Christianity being the "American religion," causing them to look to other religious influences like Chondoism.)
In a TL with a socialist or USSR-aligned Israel, I think an alternative option for the Kims would be to actively promote Judaism as "socialist Christianity," leading to it being the foundation of their new state ideology, "Jewche."