I seem to remember reading that the Khazars only converted to Judaism, to avoid converting to Christianity or Islam (thus angering their neighbours, Constantinople, Kiev or the Muslim Caliphates); as well, it was mostly only the Upper class Khazars that converted. The rest of their population was primarily Muslim, or followers of Tengrism.
If the Magyars DID convert to Judaism, I would think it would mostly be the upper echelons of their society that did, just like with the Khazars; the rest of the population would worship traditional faiths, and then likely would convert to Catholicism, as the OTL Hungarians (Magyars) did.
It could be interesting; maybe the Magyars that converted to Judaism would convert to Catholicism later on, or maybe they won't. That could possibly lead to a split in Magyar society, possibly leading to a 'purge' of those elements in their society that are connected to Judaism.
Anyway, that's just my two cents.