Not necessarily true. India is not a truly secular democratic country, no matter what some would have you believe. Hindu nationalists are present in large number and still hold sway in a few places. It's not a Hindu country either but regardless, religion is big over there.
A true secular democracy would be Canada. Over here, the leader of our third party is Jagmeet Singh, a practicing sikh who wears a turban, carries a kirpan and because of his speaking out for the atrocities committed against sikhs in India, has been banned from entering the country of his parents' birth.
So yes, a sikh can become the PM of Canada in a couple of years, and it's also possible that in a few years we'll have a Muslim PM as well. It can be done but not in India, at the moment.