They don't have separation of church and state because the state dictates a very limited expression of religion.
But if they let everyone join any wackadoo religion (the more the better) like they do in the US, would they not have people thinking about the next life and not concrete political problems?
It seems to me that if religion were taken out the picture in the US that many people would become much more politically active. More focused on money and labor issues. Not all of this render unto to Caesar bullshit. Perhaps not all for what many consider the best.