This would have more to do with the first Amendment. Some government entities have responded by allowing no religious iconography. Other’s have responded by opening up property to being available to both religious and non-religious iconography. Remember that in part the first amendment prohibits giving preference to one religion.
Nope, that’s private property, not government property. First Amendment also protects the rights of a Church to have their name displayed on their sign by prohibiting laws impeding the free exercise of religion or abridging the freedom of speech.
Main article: Establishment Clause
Thomas Jefferson wrote with respect to the First Amendment and its restriction on the legislative branch of the federal government in an 1802 letter[9] to the Danbury Baptists (a religious minority concerned about the dominant position of the Congregationalist church in Connecticut):
Believing with you that religion is a matter which lies solely between man and his god, that he owes account to none other for his faith or his worship, that the legitimate powers of government reach actions only, and not opinions, I contemplate with sovereign reverence that act of the whole American people which declared that their “legislature” should “make no law respecting an establishment of religion, or prohibiting the free exercise thereof,” thus building a wall of separation between church and State. Adhering to this expression of the supreme will of the nation in behalf of the rights of conscience, I shall see with sincere satisfaction the progress of those sentiments which tend to restore to man all his natural rights, convinced he has no natural right in opposition to his social duties.
In Reynolds v. United States (1878) the Supreme Court used these words to declare that "it may be accepted almost as an authoritative declaration of the scope and effect of the amendment thus secured. Congress was deprived of all legislative power over mere [religious] opinion, but was left free to reach [only those religious] actions which were in violation of social duties or subversive of good order.” Quoting from Jefferson’s Virginia Statute for Religious Freedom the court stated further in Reynolds:
In the preamble of this act …] religious freedom is defined; and after a recital ‘that to suffer the civil magistrate to intrude his powers into the field of opinion, and to restrain the profession or propagation of principles on supposition of their ill tendency, is a dangerous fallacy which at once destroys all religious liberty,’ it is declared ‘that it is time enough for the rightful purposes of civil government for its officers to interfere [only] when [religious] principles break out into overt acts against peace and good order.’ In these two sentences is found the true distinction between what properly belongs to the church and what to the State.
Originally, the First Amendment applied only to the federal government, and some states continued official state religions after ratification. Massachusetts, for example, was officially Congregationalist until the 1830s.[10] In 1947, the U.S. Supreme Court decision Everson v. Board of Education incorporated the Establishment Clause (i.e., made it apply against the states). In the majority decision, Justice Hugo Black wrote,
You see when our government forces a Religion/Church to do what is against Religious/Church Dogma, or considered/known to be in complete violation of Religion/Church opinion or practice, this is illegal. The Religion/Church is the people its members who profess its faith. The Religion/Church is not the building it meets in or its writings. Those are the comforts and professed truths of the Religion/Church which is the people or human members. When the government stands by and does nothing to advert this infringement, the government must have decided to ignore the Constitution and is in violation of the law.
The “establishment of religion” clause of the First Amendment means at least this: Neither a state nor the Federal Government can set up a church. Neither can pass laws which aid one religion, aid all religions, or prefer one religion to another … in the words of Jefferson, the [First Amendment] clause against establishment of religion by law was intended to erect ‘a wall of separation between church and State’ … That wall must be kept high and impregnable. We could not approve the slightest breach."[11]
I believe, the state has sorely breached this wall.