Christianity is a very weird one. For example, the Christianity that emerged in the period was what we call Orthodox Christianity, and is very different from Catholicism.
Same tree/base class. Orthodox/Catholic/Protestant diffs are no bigger than Shia/Sunni or Mahayana/Theravada or Vaishnavism/Shaivism. In fact the range of Christianity is narrower not wider.
I can't speak about Shia/Sunni splits nor the other ones. But the basic beliefs of Orthodoxy are very different from Catholicism. And I feel I have more in common with a Buddhist than a Mormon. And I can't even begin to understand Evangelical Protestantism.
And given what you said - Islam is about different from Orthodoxy as Mormonism and some flavors of Protestantism. Heck I could make a claim there is more affinity with Islam and Orthodox Christianity than most Christian faiths.
To my original point, I define “traditional” as “roots in the peculiar conditions of the axial age”
Note that no new religions with unrelated roots in post 800 AD events have survived.
Perhaps Protestantism is indeed very different from Greek Orthodox. But both trace to life of Christ in mid-axial age.
By contrast take Scientology. Or Baha’i. Came later, not more than marginal status. They’ve taken essentially no market share from trad religions.