The Yuan dynasty were ruled by the Mongolians. The Mongolians were devout Buddhists and revered the Tibetan Buddhists. The search for reincarnated Tulkas by the Tibetan Buddhists would extend into the Mongolian regions. The imperial family gave a lot of autonomy to Tibet.
The last Imperial dynasty, Qing, was ruled by Manchurians. The Manchurians were a foreign, non-Han ethnic minority, and the imperial family were also devout Buddhists. The Qin emperors gave the Tibetan region autonomy, though they asserted state power by changing the selection process of the lamas back in the late 1800s.
My point is that, even if I disagree with how the CCP is wiping out the Tibetan heritage, this is a outgrowth of centuries of interactions, religion, and politics in that region.
I could also talk about the many ethnic groups in Napal and Himalayan regions, from which the Tibetan Buddhists assimilated many of the shamanic traditions of the region. From those Himalayan shamans perspective, the "lamaists" ganked their traditions and practiced them for the betterment of themselves rather than the betterment of the community. (From the Tibetan Buddhist perspective, those practices were reified within the View of Mahayana, for the betterment of all sentient beings).