From my limited understanding, one of the reasons why rulers converted was because of the political benefits. Becoming Catholic or Orthodox or Sunni not only unlocked foreign support, but the institutions of those churches (yes, I know that Sunni Islam doesn't use the word) served as a parallel hierarchy that the rulers could play off against their vassals to increase their own power - or something like that, I'm not an expert.
Depends on how early you're starting tbh, as well as where you're looking. For example, in England, if Aethelbert of Kent doesn't marry a Frankish princess he's unlikely to convert to Christianity, but by that point Wales is strongly Christianised. Perhaps if stronger ties develop between the Saxons and those in what would later become Scotland you'd see less incentive for either to go Christian, and the success of the missions to Ireland in the 6th is hardly guaranteed. Even if they did, with the Saxons remaining pagan you could see Insular Christianity becoming more of its own thing without a direct line to Rome.
Meanwhile, Volga Bulgaria became Sunni partly because Almış wanted the Caliph's help in becoming independent of the Khazars. If the Khazars were weaker then Almış wouldn't need the Caliph's help, but conversely the Khazars themselves would be more vulnerable to Islam spreading from Dagestan northwards - if the Arabs failed to penetrate as far into the Caucasus as they did in the eight century then that would avert that, though that could just mean that the Volga Bulgars would appeal to the Byzantines instead if the Volga Bulgars are still a thing TTL.
tl;dr it's complicated and I'm not an expert.
