There are hybrids
From articles below:
In India it is difficult to be an atheist. Your religion is noted on your birth certificate to start with, and for example laws for marriage, divorce, inheritage are not secular, but depend on the religion you have. How that goes with interfaith marriage IDK.
In Indonesia that interfaith marriage is simply forbidden. When you are raised, you have to follow the education of one of six religions and are locked in.
When you look at the development of post WW2 of more and more people in the West practicing less up to becoming atheists, hybrid marriages are assumed playing a role (is this process BTW still going on everywhere ?). These countries are build on religion building blocks.
The western approach of a secular state with freedom of speech and freedom of religion, as platform for individual choices, is handled in these countries in another way. Blasphemy is a severe violation of the law. That christian governor two years ago had no chance for his re-election when (fake) accused of blasphemy. No need for a theocracy, with a divinely inspired government, if you are in control. Freedom of speech is a corner stone of the secular state (whereby I think it improves with some limits, but each of those limits can be very tricky, depending on the country culture in general)
There are at this time in history no such hybrid examples for christian state hybrids AFAIK. But you could see Greece as a pious democracy. Clergy are paid by the state, education (lower level) is done by the church, even building permits need clergy approval.
https://www.pri.org/stories/2012-12-10/why-its-not-easy-be-atheist-india
https://theconversation.com/is-indonesias-pious-democracy-safe-from-islamic-extremism-79239