I have the feeling that we who've grown up in Western countries with ideas of separation of church and state tend to accept the status quo we've seen at face value, and not question so much whether it really is a separation of church and state.
I'm also from the UK where I think we're fairly proud of our separation of church and state. Then I moved to Germany and found it really weird - the state, to me, is bound to Christianity in a way that I found quite uncomfortable. For example:
* The state collects a church tax. You only have to pay it if you're a registered Christian (and you can be a Christian without registering) but essentially a portion of your paycheck automatically goes to the church via the state.
* To become a pastor or priest, or one of certain other religious roles in one of the official churches in Germany, you have to complete an exam set and managed by the state (a Staatsexamen).
* In schools, Christian children get taught a special Christian course. In fairness, this is again opt-in, but it's again a state-set course taught by state-approved religious educators.
To me, this all feels wildly inappropriate for a nation that claims to have a separation of church and state. But to my wife, this is perfectly normal and a healthy separation between the two organisations. Meanwhile, she's horrified by the ties between church and state in the UK:
* Many state schools are run by Christian organisations, or have explicitly religious board members. Moreover, state schools are expected to have a certain amount of Christian "collective worship" - typically, this means a children's hymn once a week during an assembly.
* The state chooses bishops. Typically a shortlist is organised by the church, but the Prime Minister can (and has once in living memory) veto a candidate for political reasons. They are also involved in the selection of candidates, but less so.
* The state still makes laws directly involving the church. One of the outcomes from the discussion on gay marriage was that, while gay marriage was legalised, the Church of England specifically was banned from performing those marriages, to make prevent issues where people might sue the CoE for discrimination. There are plenty of other more historical laws but this is probably one of the more egregious examples in modern times of the state legislating to control the church.
I think sometimes, growing up in the West, we accept the dogma of separation of state and religion without really asking how true that really is. In reality, Christianity is deeply intertwined with most European constitutions and state apparatuses. We just have a consistent blind spot for these cases, where they're a lot easier to see when viewing from afar.