> Outside of the sliver of people that research religion that remain religious...

I come from the rural area of a developing Muslim country (Bangladesh), most people around me didn't have much secular or religious education, and yet I think absolutely everyone around me knew Islam is a continuation of Christianity.

The idea is that current generation of Christians have lost their way (and one of their greatest sins is worshipping Jesus), that's why God had to reveal Islam, but the "true Christians" of past were righteous and worshipped the same God as ours.

I think you're not aware of how big a deal is shirk- the idea of attributing God-like power to humans- is in (Sunni-) Islam.