For some clarification, why do you think tolerance of Islam wouldn't be compatible with the Mandate of Heaven? The Mandate of Heaven was, by and large, a tool for establishing legitimacy for rulers. The Tang and Song were also tolerant of Islam (although the Tang did have some real difficulties with Buddhism). I'm a bit confused as to why you think they are incompatible?

Hey I will try to take a stab at this, though I am only a 4th year undergrad student. You seem to be viewing the mandate of heaven as similar to divine authority. They are not the same. While in Europe as seen with the Reformation, anything that questioned the total authority of Christianity questioned the authority of the king and had to be shut down. The mandate of heaven did not work in this same way. What the mandate of heaven was can perhaps be equated to Rousseau's social contract. The ruler was a ruler because he was fit to be the ruler he was not the head of a religious institution. China has a history of religious diversity in their religions being more ideological and based on respect not entirely on a god that passed on power to the ruler. The mandate of heaven comes from heaven which is not fully an entity but more a force and any who subscribe to that force theoretically are just and can rule. So having Islam or Buddhism within the country presented no problem to authority and was tolerated for that.

An interesting side not is that China had a tendency to be for fairly tolerant in the Ming dynasty. When the printing press made its way to China under Ming rule jnstead of shutting down shops and burning books like their European counter parts what the Ming did was enforce a reading list. Instead of making it illegal to read certain books they made it so many people who read/bought books had to have a few certain ones. I forget which ones but Timothy Brook in his book "Confusians of Pleasure: Culture and Commerce in Ming China" describes this period quite well.