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They destroyed half of Eurasia without even blinking, and they were buddhists.
It appears that Ghengis was essentially areligious, unless the priests could guarantee his physical immortality as he neared old age. Before that, he essentially had no faith in anything other than himself. If anything he shows more respect toward Taoists than Buddhists, but even tolerated Islam if the Islamists did not revolt against him.
From Wikipedia:
Spirituality
Genghis Khan towards the later part of his life became interested in the ancient Buddhist and Tao religions. The Taoist monk Ch'ang Ch'un, who rejected invitations from Sung and Jin leaders, traveled more than 5000 kilometers to meet Genghis Khan close to the Afghanistan border. The first question Genghis Khan asked him was if the monk had some secret medicine that could make him immortal. The monk's negative answer disheartened Genghis Khan, and he rapidly lost interest in the monk. He also passed a decree exempting all followers of Taoist religion from paying any taxes. This made the Taoist religion very powerful at the expense of Buddhists. Genghis Khan was by and large tolerant of the multiple religions he encountered during the conquests as long as the people were obedient. However, all of his campaigns caused wanton and deliberate destruction of places of worship.[10] Religious groups were persecuted only if they resisted or opposed his empire.