One reason (or excuse) for this persecution is a widespread perception in these countries that Christianity is a "foreign" religion that has no real roots in either country. This perception should not be totally surprising, given that large-scale efforts to convert the people of India and China to one form of Christianity or another did not really occur until relatively recently in these countries' histories--in the 16th century for Catholicism and the 19th century for Protestantism. Moreover, those efforts often occurred in the context of Western imperialism and/or colonialism, making the whole Christianity missionary effort suspect in the eyes of many in both countries.
The truth, however, is that the history of Christianity in both countries goes back much further than the last few centuries, and this fact can be demonstrated in a number of ways. For example, in the case of India, there has long been a tradition among the so-called St. Thomas Christians in the state of Kerala that the Apostle Thomas--the famous "doubting Thomas" who questioned the reality of Jesus' resurrection until confronted with the risen Lord--traveled to India in the first century AD. He is said to have converted a number of the local people, but ultimately suffered martyrdom for his faith. In addition to this longstanding tradition, a number of historical discoveries over the years strongly suggest that this story contains at least a kernel of truth, as William Dalrymple documents in an article appearing in the Apr. 14, 2000 issue of The Guardian. For instance, archaeological and documentary evidence demonstrates that the Romans were engaged in an extensive trade with India during the first century AD, meaning that Thomas could have traveled from the Middle East to India with relative ease.
As for China, the famous Xi'an Stele, dating to AD 781, is evidence of the presence of a form of Christianity in China nearly a millennium before the arrival of the first Catholic and Protestant missionaries. This large stone tablet was erected by a Nestorian missionary named Yazdhozid in the then Chinese capital of Chang-An (present-day Xi'an). The Nestorians took their name from Nestorius (386-451), a patriarch of Constantinople. They held to the belief that the human and divine natures of Jesus were separate, not unified--a highly controversial position rejected by most churches. The Nestorians were zealous in promoting their faith throughout the Persian Empire and Central and East Asia during the seventh and eighth centuries. As a result, Nestorianism reached China during the Tang Dynasty (618-907). According to the inscription on the Xi'an Stele, in AD 635, the Tang emperor Taizong personally received a Nestorian bishop named Alopen at court. He invited Alopen to translate the Christian scriptures into Chinese and eventually authorized the establishment of a Nestorian church in the capital Chang-An. How the Xi'an Stele was lost and rediscovered, and the ultimate fate of Nestorianism in China is recounted in an informative article by church historian T.N. Ho which appeared in the Nov. 11, 2o22 issue of Christianity Today.
In light of this evidence, it should be clear that Christianity--despite not originating in India or China--has fairly deep roots in the histories of both countries. Indeed, in the case of China, Christianity has a longer history than Communism and has been around almost as long as Buddhism (which some Chinese once rejected due to its foreign origin)! Of course, the persecution of Christians in India and China would not be justified even if Christianity were of recent origin in either country, but the actual history of the Christian faith in both countries demonstrates that it has been present in India and China for quite a long time.
Image: 16th century Portuguese drawing of St. Thomas Christians in Inda, from Wikimedia Commons