Is there a word for the process of applying heavenly-derived arguments to terrestrial issues? For example,
"John Doe argues against abortion because his Catholic faith says it's wrong. John's argument is X-ical."
Where X is something like tautology. I feel the word "religious" doesn't sufficiently convey the incongruity of using out-of-this-world logic to this world.
If you are looking for something akin to tautology, then perhaps "begging the question", which means "begs that the conclusion be admitted as an axiom," rather than the modern (typical) usage "forces me to ask" that one sees everywhere anymore.
If you feel frisky, you might call it an "appeal to (false) authority." which means that the authority is being given a pass on veracity without actually meeting a standard of proof.
It is not necessary for you to wrap your critique in the idea of religion, the fallacy you are attempting to point out is agnostic.
Dogma is defined by Cambridge as
a fixed, especially religious, belief or set of beliefs that people are expected to accept without any doubts
It and other dictionaries I've consulted, say the word, and its associated word "dogmatic", is used to express disapproval. However the Roman Catholic Church does refer to its own teachings as dogmas, if they are authoritatively defined teachings of the Church.
Oxford gives the origin of dogmatic as denoting a philosopher from a school based on a priori assumptions. In this sense an argument is dogmatic if it is based on assumptions which cannot be challenged because they are held to be certainly true.
If Mr Doe says that abortion is wrong because God says so, or the Pope says so, or he believes that the Bible, correctly interpreted, says so, then his argument is dogmatic.
Mr Doe may put forward other arguments against abortion, such as the risks involved, the loss of human potential, the emotional trauma etc. and it may be that, for Mr Doe, these arguments would be spurious since in reality his objection is purely dogmatic. It would be pointless trying to convince him that the risks could be minimised or the world is over-populated because the reasons he gives are not at all relevant to his position. For him personally, his only real objection to abortion is dogmatic. It might be possible, depending on his denomination, to argue from the Bible that abortion is permitted.
In many fields of mathematics we would say certain propositions are axiomatic. Other statements can be proved or disproved based on deduction from the axioms but the axioms cannot be challenged.
We could say
John's argument is dogmatic.
ecclesiastical
not secular
http://www.dictionary.com/browse/ecclesiastical
metaphysical
concerned with abstract thought or subjects, as existence, causality, or truth.
concerned with first principles and ultimate grounds, as being, time, or substance.
