Tibetans are not unified by language or religion. There are more than a dozen Tibetic languages, and speakers of more distantly related language families like rGyalrongic are also classified as Tibetans by the government. The official policy of one standard language per recognized ethnicity does mean that many of them will have been educated in Lhasa Tibetan at school.
On the religion front, next to the various schools of Tibetan Buddhism, there's also the older Bön and other, less popular religions like Islam.