Is this an appeal to authority?

I had an argument with some people on the internet about separation of church and state a little while back, and they argued: "The government says that the church and state are separate, therefore, the church and state are separate." I told them that this was an appeal to authority, and they said that it wasn't. Is this an appeal to authority?

The claim "the church and state are separate" is source-dependent, meaning the truth of the claim is not based on a fact of reality, but rather it is based on an authority. Both parties need to agree on the legitimate authority for this claim. For example, "Do you agree that if the Constitution of the US explicitly states that 'the church and state are separate' then the church and state are separate?" Now we have created a falsifiable claim in which authority does matter.

Consider the argument, "It is mandatory to wear a mask when in public and 6' distance cannot be maintained, because my local government says so." We are appealing to authority here, but most would agree that this is a legitimate appeal because the local government has the right to make such laws. Of course, one can disagree with the politics, but the reasoning is still good.

So yes, it is an appeal to authority but not necessarily a fallacious one. The error in this debate appears to be the failure of both parties to establish the legitimate authority on the claim.

There is also a problem with ambiguity here. Michael's answer here does a good job at explaining the complexity of the claim.

Yes. it is an Appeal to (false) Authority fallacy in that it incorrectly and deceptively identifies "government" as the author of church and state separation rather than the actual and idealized interpretation of The Establishment Clause by Thomas Jefferson and other founding fathers.

Interestingly enough, the exact wording "separation of church and state" does not exist within the framework of the Constitution. President Thomas Jefferson famously employed the term in a letter to a group of Baptists in Danbury, Connecticut. 

"Our nation’s founders disagreed about the exact meaning of “no establishment” under the First Amendment; the argument continues to this day.

But there was and is widespread agreement that preventing the government from interfering with religion is an essential principle of religious liberty. All of the Framers understood that “no establishment” meant no national church and no government involvement in religion.

Thomas Jefferson and James Madison believed that without separating church from state, there could be no real religious freedom.

The first use of the “wall of separation” metaphor was by Roger Williams, who founded Rhode Island in 1635. He said an authentic Christian church would be possible only if there was “a wall or hedge of separation” between the “wilderness of the world” and “the garden of the church.” Any government involvement in the church, he believed, corrupts the church.

Then in 1802, Thomas Jefferson, in a letter to the Danbury Baptist Association, wrote:

“I contemplate with sovereign reverence that acts 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.”

It's Appeal to Authority. The issue with the statement itself is that the government claiming that the church and state are separate or even the law stating that it should be doesn't necessarily mean it actually is in practice. If we're talking about the US government specifically, a lot of politicians and legislation assume 'Christian values' and impose them on others, which is an example of church and state not actually being separate despite claims otherwise. The whole idea of separation of church and state is meant to avoid giving religions political power like and all the control it's historically afforded them in past empires and dictatorships.

This is a tricky one. For example how do we define as Church and state being separate? It is the constitution?

Is it the lack of Christian/Bibilical laws in the states law? Is it the formal law claiming so?

Or is it the lack of religious leaders in the government. I would say an empty statement such as "the government says so" needs to be be verified by the law. By the lack of Church authority in public life and state laws.

If not, then it can be at best a mis-characterization of the concept of Church and state being separate.

The US government is based on the constitution. The constitution is a formal cause as a device to materialize the final cause described in the Declaration of Independence. All of the above recognize the people as the sovereign and the political structure of the US as fully representative constitutional republic, with direct democracy elements in small enough administrative units. 

The sovereign says the church and state are separate. Because the sovereign has the authority about the matter, the sovereign is the source of knowledge. It is not possible to know from other source. There is not a fallacy.

We can then look at the matters of definition (what does the separation mean), application, enforcement of the rule, etc. Can we find a fallacy there? 

Hardly. The nature of a constitutional order does not allow immediate and precise application. The declaration has said all men are created equal. Abraham Lincoln emancipated the slaves in the 10 southern states. But there were as many as 9 free states 50 years before the Civil War. Some other states were working around slavery with implication of regulations, etc. 

So far so good. We can say so because there is the Rule of Law in the US. What happens if there is not the Rule of Law? Then we can find fallacies.

The constitution of the USSR was ratified by the "soviets." Soviet is a Russian word for "worker-soldier councils," hence a group of people. It was not clear the group was by actual occupation or self-identification. However hard you might try, it was not possible to pin down the sovereign. A reference to the USSR constitution had to be a reference to the text itself. It had to be the fallacy of appeal to authority. 

It is easy to take things for granted now but there was a time a communist empire was a global superpower. If you want a sense of it, take a look at its constitution:

https://en.wikisource.org/wiki/Constitution_of_the_Soviet_Union_(1977,_Unamended)