(As per K&G youtube channel) I learned that when it comes to believe system, the Mongols believe that everyone worships the same god, Tengri, but in varied way in every culture/religion they encounter.

They believe that as long as everyone submit themselves under the Mongol rule, it means they obey Tengri/Mongolian god.

There are various religious communities inside the empire but they also don't bother to do the worst thing possible to obliterate anyone who doesn't submit to Mongol, regardless their believe.

But I think in a smaller level it's also not as simple/straightforward as that. Mongolian Shamans also known to have conflicts with the Khan. Sometimes the Khan kept asking the Shamans to do a ritual over and over again until the result aligns with the Khan's desire. Or sometimes the Shaman (being a regarded class in their society) have their own political motive to do something against the Khan.