Why don Chinese accept the fact that Yuan Dynasty was Mongolian Dynasty?
Of course they accept it was a Mongolian dynasty (and Qing a Manchu dynasty). It’s just that they less than one hundred years ago redefined the Mongolians and Manchus (among others) to be included in the “Chinese” people. Hence, the words Mongolian and Chinese don’t contradict each other. It’s actually quite ironic, when after successfully having struggled to liberate China and get rid of the allegedly “foreign” (= Manchu) rulers in the early 20th century, they soon after redefined them as a since beginningless time integrated part of the Chinese people. If, on the other hand, you check what the official history writers at the time wrote, they certainly don’t include Mongolia (or Tibet or Xinjiang) in China itself, just included in the Empire that also ruled China. This you can see for example in the official history of the Yuan Dynasty, written the year after the fall of the Yuan Dynasty, just as in the official history of the Ming Dynasty, written just after the fall of the Ming.