To what extent was Islam religion able to gain converts from the indigenous Hindu and Buddhist populations?
Islam gained a ready following among many Hindu Indian groups; but was less successful with Buddhists. The Islamic principle of all being equal in the eyes of God readily appealed to the lower castes and out castes who suffered under the Hindu Caste system. Since Buddhism did not recognize the caste system, followers of that religion did not convert so readily; rather conversion typically was the result of conquest during which Buddhist temples were destroyed.
The large majority of converts, both Buddhist and Hindu were due to the work of Islamic missionaries known as Sufis. Sufis followed a mystical form of Islam and promoted personal devotion to God; but at the same time did not insist that new followers abandon all old beliefs; in fact they allowed customs such as veneration of spirits and ancestors, all part of long held traditional beliefs. The promotion of a religion that offered a personal form of comfort and meaning (which neither Buddhism nor Hinduism offered) led to a large number of converts.