In this the US still mostly adheres to this. Not perfectly nor without prejudice, but mostly you can recognise the intention.

Although the UK does favour certain religions, even granting some of them representation in the House of Lords (for goddess alone knows what reason), by and large, our laws are indifferent to religion even if it is as not as much as we like. I was very pleased to discover last year that I had not previously known that Michael Howard (Tory leader 2003-5) was jewish, as it had been something of such little consideration to his position that it had never been mentioned.

Only Blair made a point of letting us know he was religious, just so he could then let us know he "didn't do god".

keep to the Fen Causeway

Thus freedom became an assertion of the individual's right to pursue his own vision, and liberty became a prior demand for all human speculation or education. This demand did not lessen as the Hellenic world spread and was transmuted by Christianity. In fact, the Christian emphasis on the individual soul's worth, and its otherworldly goal, deepened the cleavage between man and the religious state. The Christian recognizes a divided loyalty, giving to Caesar what is Caesar's, but to God the inestimably vaster reaches of the soul that belong to God.

But if the state's order is no longer, in the Greek world, coextensive with man's attempt to order his private world, what role is government to play? Where does the supremacy of the private person find its frontier, or verge on other claims? How do the sacred areas of each man's individuality meet and adjust to each other? It is this question that has put the problem of freedom at the center of Western political dispute. And, in a kind of slovenly philosophical shorthand, this problem has been cast as a search for the amount of freedom man is to enjoy. But the problem is that the Greek world introduced an entirely new conception of human life, one still novel today, a conception that runs into contradiction if pushed by a ruthless logic. The autonomy of the individual, the fight against tradition, seem to make government at worst a causeless evil, at best a necessary evil. But experience has taught that a "freedom" which travels down the road of anarchy is never seen again. Thus the problem of the Western world has been to find a new kind of order to act as a foundation for its fugitive new kind of freedom. Many attempts at the solution of this problem have been short-lived because they did not come to grips  with the particular kind of freedom-with its almost impossible demands-that the West has chosen to pursue. The attempts which remain in the central line of Western experiment cluster into two main groups. These continuing schools of thought, or lines of approach, correspond in some degree with the popular division of political thinkers into liberal and conservative. I

I-religion...

'The history of public debt is full of irony. It rarely follows our ideas of order and justice.' Thomas Piketty

In Japan, it is tricky to think about separation of church and state, because those have not been merged together in the familiar (to us) ways in the first place. Yes, Buddhism was used as a spiritual training of samurais, WWII officers, and now of corporate management. And some ministers and parliament members savour stirring East Asian commotion by visiting the Yasukuni Shinto shrine. But that does not look like typical (for Abrahamic religions?) manipulation by faith, social pressure to conform or mass psychosis. Japan is historically a very hierarchic society - was it ruled without an ample assortment of fantastic stories? What role did natural isolation and hazards play?

In a more recent study, Hadaway estimated that if the number of Americans who told Gallup pollsters that they attended church in the last week were accurate, about 118 million Americans would be at houses of worship each week. By calculating the number of congregations (including non-Christian congregations) and their average attendance, Hadaway estimated that in reality about 21 percent of Americans attended religious services weekly--exactly half the number who told pollsters they did.

Finally, in a brand new paper, Philip Brenner at the University of Michigan's Institute for Social Research compared self-reported attendance at religious services with "time-use" interviews in the United States, Canada, the Netherlands, Germany, France, Norway, Finland, Slovenia, Italy, Spain, Austria, Ireland, and Great Britain. Brenner looked at nearly 500 studies over four decades, involving nearly a million respondents.

Brenner found that the United States and Canada were outliers--not in religious attendance, but in overreporting religious attendance. Americans attended services about as often as Italians and Slovenians and slightly more than Brits and Germans. The significant difference between the two North American countries and other industrialized nations was the enormous gap between poll responses and time-use studies in those two countries.

Why do Americans and Canadians feel the need to overreport their religious attendance? You could say that religiosity for Americans is tied to their identity in a way that it is not for the Germans, the French, and the British. But that only restates the mystery. Why is religiosity tied to American identity?

But, thinking about Asia, I don't really think we can point to differences between east and west as far as your categories are concerned.  To the extent that they are valid in Chinese or Hindu regions, I can't really think of anything other than state-specific variances from Judeo-Christian or Muslim regions.  It may well be that the issues of secularization, freedom of conscience, and church-state separation have more to do with resolving the historical problems of governing multi-ethnic/multi-religious polities than anything else.