in every instance, nomads would adopt a different religion from the people they raided or ruled over
in Europe, the Golden Horde was Sunni while the Russians were Orthodox
in central Asia, the Timurids and other Turks were Sunni while the Iranian settlers were Shia
in eastern Asia, the nomads would be Buddhists while the settlers were Confucian
why?
in most cases of settlers migrating to conquer settlers, the conquerors would eventually adopt the religion of the conquered.
Khazars seem to have adopted judaism explicitly BECAUSE their neighbors were all either christian or muslim
Magyars adopted Christianity, but only AFTER they settled and became agriculturalists
I can't comment on other instances since I'm only familiar with the Golden Horde situation, but basically it was a continuation of the Imperial Mongol policy of disregarding settled peoples and focusing on colonization and subjugation of steppe [1]. Of course, Mongols and their successors did actively attack, plunder, occupy and vassalize settled countries, but they primarily used them as sources of income, labour, technology and additional supporting troops while other nomads were considered to be either future slaves or subjects ready to be integrated into proper Mongolian society. This was one of the reasons why Tatars from the Golden Horde took southern steppes and didn't found cities or take inhabited lands away from Russians: their plan was to remain in control and in closer proximity to the nomadic territories, thus distancing themselves from the possible influence of the conquered neighbours.
Adoption of Islam by the Golden Horde also had another approach: it was a major religion of their neighbours, including Hulaguid Dynasty in Iran (although it fell quickly after The Golden Horde's adoption of Islam), and since they tried to distance themselves from the western feudal kingdoms, it was only logical to adopt another religion instead of Christianity. Although this decision wasn't completely decisive: Uzbek-khan's daughter Konchaqa, who married Moscow prince Yuri Danilovich in 1317, was baptized as a Christian, and later it wasn't uncommon for Tatars on Russian service to change their religion.
In this case adoption of Islam by the Golden Horde was partially because of their large distance away from large Christian centers and also because of growing Islamic influence in Asia.