This question has to be addressed on a case-by-case basis. The country in which I live, the UK, has no church/state separation, but this does not make us undemocratic. For example:
- The Church of England is the established church in England, the sovereign is its supreme governor, its 26 most senior bishops sit in the House of Lords, and its three most senior bishops are members of the Privy Council.
- Prayers are said every day in the House of Lords (by a bishop) and the House of Commons (by the speaker’s chaplain).
- Every order of chivalry has a prelate/dean/chaplain, who is always an Anglican bishop or priest or Church of Scotland minister, and a chapel, which is always an Anglican or Church of Scotland church.
- The sovereign is a member of the Church of Scotland and either attends the General Assembly or is represented by a Lord High Commissioner. The first formal act undertaken by the monarch is the swearing of an oath to “maintain and preserve the Protestant Religion and Presbyterian Church Government” (in Scotland).
- The sovereign is always crowned by the archbishop of Canterbury at Westminster Abbey.
- Every person in England and Wales has the right to be married in their Anglican parish church, even if not a member of the C of E or Church in Wales.
- The archbishop of Canterbury is authorised by Parliament to confer academic degrees upon persons owing allegiance to the British monarch.
Thus it can be seen that in the UK the lack of any church/state separation has little impact on most people’s everyday lives.
The impact of the establishment of the C of E is probably more apparent to those who are members of that church. For example, bishops and other senior members of the clergy are at least notionally appointed by the monarch, and bishops cannot be consecrated without something called “the Queen’s Mandate”. Some parish priests are also appointed by the Crown, the Duchy of Lancaster, the Lord Chancellor, etc. The church is governed by synodal legislation known as “Measures”, which have the force of Acts of Parliament and can be enforced in English courts, whose decisions can be appealed to the Judicial Committee of the Privy Council. Thus the church is to some extent subordinated to the state.
Some secularists point out that the UK and Iran are the only two countries in the world where seats in the legislature are reserved for clergy. However, the bishops generally attend and vote in the House of Lords quite rarely, and their impact on legislation is negligible. It also offends me more that 92 hereditary peers sit in the House of Lords than it does that 26 bishops do.
Therefore, many British people feel that the relationship between church and state is in fact beneficial. The negligible impact of the church on state affairs is tolerated in part because the established C of E and national Church of Scotland are moderate forms of Christianity. Furthermore, they are to some extent moderate forms of Christianity
because they are established/national churches. It seems likely that a disestablished C of E would possibly become much more liberal or much more conservative or would split into two or more rival factions.