"Secularism - The belief that religion should not influence or be involved in the organization of society, education, government, etc."

I disagree with you on your basic premise which is that India is a "Secular" country. The truth is we have never been a secular country. Indian version of secularism is more about pandering to all the whims and wishes of minority communities.

I believe true secularism is about separating religion from the state, as in, not letting religion influence the government.

The accurate model of secularism is the French model or Laicite. Many European countries, especially the central European and Scandinavian countries are truly secular. Although the US has the principle of "separation of state and church" enshrined in the constitution, there's a notable Evangelical Christian influence in making policies, so it can't be considered truly secular.