Something that is pretty underrated in islamic conversion is the flexibility of Islam, like, in many cases things considered "nope" in core islamic regions (Arabia, Levant, Mesopotamia and there it goes) are/were just made fine in regions like Al-Andalus, Central Asia and India for simply cultural reasons.
I think that it is all about Islam being made by a people (the arabs) made it very flexible in terms of cultural collision, like, in the 13th Century, you can't say that muslims in Iberia lived like muslims in India, but independently of it, the two communities are equally seen as rightfully muslim communities independently of some cultural differences that were assimilated into Islam.
It's just more simple convert to a religion when you can (until a certain point) merge with your day-to-day culture and at the same time still be seen as rightfully part of that faith. And then you remember that as a subject of muslims you've a good amount of benefits from conversion, it's like a super big win-win.
There are some unifying principles, namely all positive ones that perpetuate growth. Such as admission of physical jihad, unity in monotheism, Arabic usage for holy works and alliances of sorts formed by similar civilizational narratives.
However, fine points of theology are left to opinions. There are no set strong views on many points and hence a level of flexibility exists yes. This is often underestimated, as you mentioned in historiography. The extent to which the Islamic theological and legal system was both scholarly & strict yet also mystical and flexible. It is an interesting topic, surely.