It's not complicated. Signs and symbols - including statues - are considered as being a form of speech. The intention of the First Amendment was to protect free speech by everyone, regardless of the political and/or religious leanings of their speech. Therefore, if one religious group is allowed to place a symbol of speech on government grounds then any and all religious groups must be allowed to place symbols of speech on those grounds if they desire.
Well, you mentioned the intentions, I gather of those who proposed or ratified the 1st Amendment.
The Founders were a mixed bag of Congregationalist Christians, Catholics, Presbyterians, Methodists, Episcopalians and Deists.
In the States of Massachusetts, Connecticut, and New Hampshire, the established (i.e. state-funded) religion was Congregationalism. In Maryland, Virginia, South Carolina and Georgia it was Episcopalianism (although Maryland had a large number of Roman Catholics). In Pennsylvania and Rhode Island (mainly Quakers), the diversity of opinion on sectarian questions was such that no established religion existed. In establishing the United States under the Constitution, many different opinions existed as to what should be the dominant religion of the United States. Congregationalists refused to establish the Episcopal Church. Episcopalians refused to establish the Congregational Church. Quakers disagreed with all the others. In the end, the Founders established the principle that the general government would have certain limited enumerated powers (strictly limited to those enumerated in the Constitution) and the states were sovereign within their functional realms. Establishing a religion was not among the powers granted to the general government, therefore, it was absolutely prohibited from establishing a national Federal religion.
The states, in their turn retained absolute sovereignty over the matter of established religion.
Connecticut retained it established religion until 1818. (note that if the 1st amendment outlawed state religions, this would not have been possible). Massachusetts retained it until 1834. New Hampshire retained Congregationalism until 1877. (North Carolina's constitution
to this day makes it illegal for an atheist to hold public office.) If the I Amendment had done this, then disestablishment would have been superfluous. Those proposing disestablishment would have just said, "We did that when we ratified the I Amendment." Nobody made that argument in 1818 or 1834 or 1877, because he would have been laughed out of the legislature as being too ignorant of our system of government to have an opinion worthy of listening to. No, when the states wanted to disestablish, they disestablished, each state acting for itself.
Now, some might say, the XIV Amendment incorporated the Bill of Rights and applied it against the states, so after the XIV Amendment was ratified, it meant that states could not establish a state religion. If that were true, I would ask for some statement from the period of the debates over the XIV Amendment in which some proponent of ratification acknowledged that the XIV Amendment would prohibit states from having an established religion. Nobody can provide such a statement because no supporter of the XIV Amendment at the time suggested this would be the import of the XIV Amendment. And, further, James Blaine in 1875 proposed the
Blaine Amendment:
Blaine Amendment said:
No State shall make any law respecting an establishment of religion, or prohibiting the free exercise thereof; and no money raised by taxation in any State for the support of public schools, or derived from any public fund therefor, nor any public lands devoted thereto, shall ever be under the control of any religious sect; nor shall any money so raised or lands so devoted be divided between religious sects or denominations.
Supporters of the idea would have simply said, "Jimmy, we already did that when we ratified the XIV Amendment." Nobody ever made a statement along those lines. Such was not the intention of the XIV Amendment.
So where does this incorporation argument come from? Federal judge invented it out of whole cloth in the early twentieth century and said, in effect, "I do not think any state should have an established religion, therefore, I'm ruling that the Constitution denies the states that right." The irony is that such federal judges inevitably did do extreme violence to the essential principle of separation of powers between the general and the state governments. The Founders were adamant and unanimous on
that principle.
None of that is an argument in favor of a state having an established religion (I personally do not want Virginia to have an established religion), but I do believe that the general government is supreme in those areas in which the sovereigns (the people of the several states) granted it supremacy and the states are supreme in those areas which the sovereigns failed to deny state supremacy.
And Arkansas having a table with the Ten Commandments no more establishes a state religion than calling the third day of the work week Woden's Day establishes Norse religion as the state religion or calling the eighth month Augustus' month establishes Roman civic religion.