

That’s not what that means. Separation of church and state simply means that the law doesn’t favor one religion over another. What you’re thinking of is the French formulation, known as laicite, which—you guessed it—is a French thing. It’s also based on some pretty problematic ideas that lead and have led to some pretty problematic results, so yeah.
For a non-French example, he’s the Australian constitution on the topic:
The Commonwealth shall not make any law for establishing any religion, or for imposing any religious observance, or for prohibiting the free exercise of any religion, and no religious test shall be required as a qualification for any office or public trust under the Commonwealth.
Nothing at all about lawmakers publicly adhering to a religion.
Now I kinda want to see what a surprise caliphate would look like.