In order to proceed in my quest to poke holes in some well-held notions of the nature of society, religion, and government, I have to start in a somewhat unusual place: the Dewey Decimal System. The Dewey Decimal System was an attempt, in the late 19th century, to classify human knowledge by category. Although the situation is still used, it has not always aged well, and perhaps the best example of this is the 200s, which cover matters of religion and faith. 200-289 all cover different aspects of the Christian religion, with all the other world religions clumped together from 290-299. From a late 19th century American perspective, this made sense, since well over 90% of the people one encountered would be Christian, and other religions were seen (for the most part) as mere oddities or matters of sociological interest. Although there were exceptions, the study of religion meant the study of Christian religion. And references to religion probably referred to a theistic or deistic conception of religion, as well as the attendant dogma and institutions.
I am not an expert on the details of the lives and beliefs of the founding fathers, or what the founders intent was in separating church and state. But I would guess that based on the general understanding of what religion was at the time (Christian religion, with specific dogmas, institutions and punitive actions against non-believers), that what they wished to restrict was the sectarian type of religion. To restrict all religion, are all religions references and customs, would have been impossible. In fact, this leads to something like a paradox, because government has to "establish" what religion is before deciding it can't "establish" it as an institution. And often what government establishes before disestablishing is Christianity or another definite theistic belief system. I tried to think of examples of things that could be seen as religious in some ways, and the examples aren't hard to find: many public college teach Tai Ji or Yoga, which often have an aspect that can be seen as "religious". The government actively protects and promotes certain sites and areas of great natural beauty or cultural interest, and some of these could be seen as having a religious significance towards some. Why, for example, is planting a tree not considered a religious act? In general, it seems that religious expressions that are dis/established seem to be theistic or doctrinal ones, while pantheistic religions, or non-doctrinal ones, are allowed.
But the best example of something that shows the impossibility of ever separating church and state is widespread use of the symbol of Lady Justice by the United States government. Lady Justice is the blindfolded woman holding scales and sometimes a sword that is a popular motif in art, and is fairly widely used in courthouses and other such buildings. Several years ago, there was a great argument about a judge's wish to display the Ten Commandments in a courthouse sculpture, which became a great rallying cry for much of liberaldom. And yet, the common presence of a somewhat bizarre pagan deity in many government buildings has never (to my knowledge) been challenged. (Other than John Ashcroft and his nipple-covering curtains, which is really an unrelated issue.) It could be argued that "Lady Justice" is not meant to be a religious figure, but rather an anthropomorphic display of a principle. However, that argument falls flat since...anthropomorphic displays of principles are almost a definition of religious. Lady Justice is, in origin, a religious figure, and the fact that she is probably not taken seriously to be an actual entity doesn't change the fact that she is a religious figure. I can't think of a single clear argument for why a pagan Goddess should be acceptable inside of a state building, if a statue of Moses holding the ten commandments is not. The best argument is that the symbol of justice has become so deeply entwined in our culture that it has a meaning quite apart from any literal belief in it: but this argument holds for many Judeo-Christian symbols as well. Not every reference or inclusion of a Judeo-Christian symbol demands belief in doctrine.
To really extricate all religious symbols from the government, we would have to start at the Statue of Liberty and work down to every park bench dedicated "in memory" of someone. However, this is not going to be done, but perhaps reflecting on how deeply religious symbolism is entwined into our culture will bring some enlightenment about what "Separation of Church and State" can mean.