It is very hard for the Tibetans to separate politics from religious issues because their government is already a mixture of both. His Holiness the Dalai Lama served as the political and religious leader in CTA. On top of that, His Holiness the Dalai Lama is alike the King where whatever he says is the rule and no one can have a different opinion other than his.
Anyone who has a different opinion will be treated as a traitor or a Chinese spy. It has been this way for hundreds of years ago. Hence, CTA can do whatever they like without the fear of being overthrown by the public as they have absolute power on their side.