I forget if they were Muslim when the Mongols rode over them. They may have been,in toto or, in part. The Keraits, who Chinnghis, then Temujin, also conquered at about the same time, were Nestorian Christians.Whatever they were, the Mongols would have let them worship in their own way.
ding ding ding. You have a good command of their history. The Uigher area of China is absolutely beautiful too, although it’s increasingly populated by Han chinese.