What problems did India's religious diversity pose?

The answer to this question depends to some extent upon
the time period about which you are asking.  The answer that comes most readily to mind
has to do with the time right after India became independent.  At that point, the
religious diversity in the country led to a split on the subcontinent.  At that time,
religious diversity caused the partition of Pakistan from
India.

This partition happened because of the presence of
both Muslims and Hindus in what was then India.  Neither side had enough trust in the
other for them to function well as one country.  Because of that, it was necessary for
the country to be divided.  Religious conflicts before and after the partition led to
the deaths of somewhere in the area of 1 million people.