Riding the Eternal Blue Sky is an awesome timeline, but I happen to think the Mongol khans were cooler than Turkic ones. So what if Tengriism had been reformed or consolidated at some time, causing it to be able to be evangelized? What I'm thinking is that instead of the Mongols gradually assimilating their religions to the conquered, they instead spread their religion. Of course, 'Reformed Tengriism' must respect local beliefs, or it will undermine the very reason why the Mongols were such great conquerors. What I'm thinking is that it becomes like Buddhism, which is evangelized but never quite as... vigoriously- as Christianity and Islam was. So, no Mongol forced conversions, but their shamans are indeed open to reaching out to native populations to show them the will of Tengri.
Also, two more ideas:
1. It's not reformed Tengriism at all but rather a cult of worship of Genghis. Hey, Alexander the Great didn't conquer as much as he did yet he got to become a god in S.M. Stirling's Conquistador.
2. It's not reformed Tengriism at all but rather a political effort by the Mongol overlords to try to get their subject peoples to semi-assimilate into their order. Which may include getting rid of their pesky squabbling faiths and accept the Mongol view of the world: with the Golden Family as the earthly rulers of their land.