All the separation of church and state apply to the government and government run/sponsored establishments.
I am a strong advocate of the this, as I have posted before, but there is no government agency involved here.
And even in some government controlled locations, it should not apply, in particular government run cemeteries like Arlington. The funerals/memorials/monuments/markers of Veterans should be in keeping with the believes of the Veteran. The chaplain service can be flexible enough to to provide the proper service supporting the religious belief or non-belief of all Veterans.
The government SHOULD NOT enforce any of those to conform to one particular religion, i.e. a cross as the marker for every grave. Jewish Veterans should be given a Star of David marker, if that is what is traditional (I don't know what is), and non-believers given what ever default marker is traditional.
Separation of Church and State requires that the State favor no religion in any way, treating each religious belief and non-believers equally, it does not require the elimination of religion in any way.
And the premiss of a Republic is that the majority, no mater how large, cannot take away the rights of a minority, no matter how small.
So, if a minority, even of one person, is having their rights violated, they CAN and SHOULD so what is necessary to stop that violation.
That is the vision of the Founding Fathers, regardless of their personal religious beliefs, and is what makes this country unique.
Separation of Church and State - Solus, there ain't no such thing. This is
liberal gibberish that is not stated anywhere in the Declaration of Independence nor in the US Constitution, nor in the Bill of Rights or any other Amendment. As the libs do with guns and everything else, they take over the discussion and spin it to their way of thinking with carefully crafted words and phrases that otherwise smart people adopt - words and phrases that twist or mask what should be the real discussion.
The 1A is quoted above, go re-read it, especially the
"prohibiting the free exercise thereof;" part.
THAT applies to the Feds, as well as businesses. You do not have a right not to be offended, so if you are an atheist and someone is giving a prayer on public ground, get over it. People in the minority do not have the right to limit my rights either.
BTW, there are Jewish stars over the graves of Jewish Armed Forces members, but I have no clue what atheists get, nor what Buddhists, mooslims, pagans/wiccans/whatever get. And I really don't care, that is their problem. Do not prevent me, tho, from saying God or Jesus or anything else over the grave of an American soldier who was a Christian.