Why do atheists and the irreligious care so much about the separation of church and state?

I am a (theologically) conservative reformed Christian and I am in favour of the separation of church and state in this country (although I’m not saying that the religious affiliation of politicians shouldn’t affect their political views). I think that the reason why the Church of England has become more liberal is because of government influence, which could be avoided if it was independent from the state. We live in a country where only 2 out of the 7 party leaders in parliament identify as Christian. If the separation of church and state would lead to the Church of England becoming more conservative, why are the irreligious so in favour of this? And btw I’m asking this here because I’ve noticed that a lot of the people in this sub are irreligious.