I find this topic to be a tricky one. The Supreme Court's rulings on the matter are no less confusing and contradictory, which is why I won't even go there. Where one draws the line between establishing an official religion and eroding religious freedom can be difficult. But I would contend that the purpose was not to eliminate religion from the public sphere to reduce religion to "a private matter." I would certainly see that as an erosion on my freedom of religion. It's just that this needs to be dealt tactfully, especially since a whopping 76% favor religious symbols in the public sphere. What is a great testament to that is what we already have in public buildings:
Here we have an engraving of Moses on the Supreme Courthouse in DC. Establishment of religion? Hardly! He's surrounded by Greeks and Romans. What is merely being recognized is that Mosaic law, as well as common law, both have shaped American jurisprudence.
Here is a picture I took at Jefferson Memorial a couple years back. It's a quote from Jefferson, and much to my amazement, it mentions G-d! But read the quote in its entirety. Although it mentions that freedoms are G-d-given, the state (i.e., man) is meant to ensure those rights, rather than lead to a slippery slope to slavery and despotism.
Here is a statue of Father Junípero Serra.....in the U.S. Capitol Building! But there are statues of other people, non-religious people, and that includes former U.S. presidents. Again, religion is not being established. Can people recognize that we live in a country that has had significant Christian influence, but at the same time can respect people of other religions? I don't look at this statue and say, "oh, this statue of Serra violates my First Amendment rights. Tear it down!" I think, "Serra played a role in American history, even though he was a big-time Catholic."
There are people out there who see anything remotely religious and are automatically offended--it's practically a gag reflex for them. I must have missed that clause in the Constitution that guarantees one's right not to be offended......oh, wait, I forgot; it's non-existent! On some level, people just need to develop a stomach for religious displays in public.
On the other hand, I can see scenarios in which it could become troublesome. Let's take the Nativity scene, for example. If you want to display a Nativity scene, you can do so on your own property. After all, we still have this notion called "property rights" in America. I can display my menorah on my window sill, you can put your Nativity scene or inflatable Santa Claus on your front lawn, and that's OK because that is private property. I will tell you, though, why it should not go on public property: because it's public property. That might seem tautological, but let's examine the difference between public and private property. Private property is excludable and rival, whereas public property is not. On public property, if a Christian has the "right" to erect a Nativity scene, the atheist has the "right" to kick it down. Especially when funded by tax-payer dollars, but even when not, such displays should not be on public property.
Barring such displays on public property does not infringe on one's freedom of religion, especially when you can put up such a display at your own home. And for those of you wondering, this would mean I wouldn't even want to see a menorah on public property. I don't want the government imposing my religious practices [even if subtly] on others, just like I wouldn't want Christianity imposed upon me.
Before concluding, I would like to make a distinction between religious displays in public and practicing religion in public. For one, as previously stated, not putting up a menorah or Nativity scene does not violate the Free Exercise clause. Two, if a religious group would like to hold a prayer service or ritual in a public venue, that is fine, as long as the government does not discriminate against one's religious practice, whether it'd be Christian, Jewish, Muslim, or Buddhist. The beauty of America is that we can be open about being religious and are able to express it. We should keep that consideration in mind while preserving the First Amendment in its totality, which means both the Establishment and the Free Exercise Clauses.