Hinduism and Buddhism aren't challenged by a strong monotheistic rival in the East...
Probably Nestorian Christianity will be more widespread than OTL. There were many converts in Persia at the time, and they would reach India and China too. While I'm not sure how sucessful they would be the Eastern Church will remain a greater voice within Christianity.
They did IOTL. And they had a generally more than decent relationship with Muslim authorities for a very long time. However, I concur that a stronger nestorian christianity is very likely ITTL.
Don't underestimate the Manichaeans!