Indian Prime-Ministership was held by Dr.Manmohan Singh (a Sikh) between 2004-14, which has been the longest tenure in recent times. The President's position is mostly ceremonial, but by far the most popular occupant has been Dr.Abdul Kalam, a Muslim scientist.
It's true though that Hinduism is far stronger today as a political force than it has ever been. And just as everywhere else, mixing religion with politics is not a good idea.