It is important to separate religion from the State to aid the country to function democratically. Most of the countries have more than one religious groups living in them. Within these religious groups, there will most likely be one group that is in a majority. If this majority religious group has access to State power, then it could quite easily use this power and financial resources to discriminate against and persecute persons of other religions. This tyranny of the majority could result in the discrimination, coercion. This would violate Fundamental Rights.
Another reason is to protect the freedom of individuals to exit from their religion, embrace another religion or have the freedom to interpret religious teachings differently.
Example: Untouchability in Hindu religious practice. If state power lies in the hands of Hindus, who believe in untouchability might misue the power against disadvantaged and it would be a difficult task to abolish this practice.