Probably Buddhism and Hinduism would end up being the primary competitors to Christianity, with Zoroastrian and to lesser extent Judaism (at least in parts of Arabia/Yemen/etc) likely remaining regional competitors outside of any great leaders playing a similar role as the early Caliphs.
It would be interesting to delve into what other potential religions that do not exist in our world could have arisen.
Maybe one example could be something that combines the forms of Christianity present in OTL Arabia (plus a dash of Marcionism) with the national election of the Arabs (or Romanized Arabs) as chosen via Ishmael (in place of Issac) with his nephew Esau (in place of Jacob) marrying Ishmael's daughter Mahalath to sire an alternate 12 tribes?
It would be interesting to delve into what other potential religions that do not exist in our world could have arisen.
Maybe one example could be something that combines the forms of Christianity present in OTL Arabia (plus a dash of Marcionism) with the national election of the Arabs (or Romanized Arabs) as chosen via Ishmael (in place of Issac) with his nephew Esau (in place of Jacob) marrying Ishmael's daughter Mahalath to sire an alternate 12 tribes?