The 1,300-year-old long conflict between Hindus and Muslims is rooted in their divergent theologies. Islam is a strictly monotheistic faith, eschewing trinity and incarnation. Hinduism is (at least on the surface) a thoroughly polytheistic religion recognizing many gods and goddesses. Yet these divergent views of the Divine would not have led to conflict if the Muslims had not conquered India in the late 12th century CE.
The religious issue
Hinduism is an ancient and complex faith that resists the simple definitions that could be applied to Christianity or Islam. Its teachings are interpreted by its own followers as, variously, monistic, polytheistic, pantheistic or monotheistic. This range of views is so wide because Hindu concepts of Divinity do not easily fit into those of Western religions. However, all these interpretations include what Westerners would classify as gods and goddesses.
Regardless of how Hindus view their own beliefs, from a Muslim perspective they fall under the category of shirk: the sin of polytheism, which includes not only belief in multiple gods, but acceptance of independent powers alongside the One God. Although Islam is not sinful from a Hindu perspective, Hinduism has historically, with few exceptions, been seen as sinful from a Muslim perspective.
The Muslim conquest of India
From around 1200 CE until the 16th century, Islamic Imperialism spread its hand over India and came into conflict with its Hindu subjects. Some of the early Mogul Emperors, particularly the 16th century Akbar I, were relatively tolerant towards Hindu beliefs. Others, such as his grandson Aurangzeb, suppressed Hindu practices, destroyed their places of worship and re-imposed the special jizyah tax on Hindus alone. This led to a deep-seated feeling of grievance amongst Hindus.
When India was British
Britain deposed the last Mogul Emperor in 1757 and, during the ensuing 300 years of British rule, officially extended toleration to all faiths. This did not diminish the animosity that existed between Hindus and Muslims. Although Ghandi drew on Hindu thought to declare the unity of all religions, his contemporary, Vinayak Damodar Savarkar emphasized Hindu nationalism. The Muslim mirror image of this movement was the Muslim League, which sought to establish a separate Muslim state (Pakistan) after achieving independence from Britain.
Independence and partition
When Britain granted independence to India in 1947 it was under the condition that the new country be partitioned into predominantly Hindu India and Muslim Pakistan. It was envisioned that both states would have sizable minorities of the other faith, and safeguards were supposed to have been put in place to protect them. All these precautions failed and inter-communal clashes lead to the deaths of at least half a million people and the ethnic cleansing of another 12 million. Large numbers of Muslims were forced out of India and almost all Hindus were forced out of Pakistan.
Since 1947 there have been four wars and numerous armed clashes between Hindu India and Muslim Pakistan. Most of these conflicts have centred on the disputed border region of Kashmir, claimed by both sides. In addition, India accuses Pakistan of funding terrorist groups that have carried out violent attacks on Indian civilians. Within India there have been inter-communal riots that have cost the lives of Muslims, driven them from their homes and destroyed places of worship. There have also been incidents of religious violence against Hindus by Muslims.
Despite the very real history of conflict between Hindus and Muslims, we should be aware that the same period of history has included many examples of Hindu-Muslim coexistence and even cooperation. For example, the whole period of dispute between India and Pakistan transpired while India was an active member of the Non-Aligned Movement, an international grouping dominated by the bloc of Muslim countries. There is just no simple way of describing the long, stormy relationship between Hindus and Muslims over the centuries and up to the present day.