"Red herring is a kind of fallacy that is an irrelevant topic introduced in an argument to divert the attention of listeners or readers from the original issue."
Not trying to distract at all. Lets tease out what is being discussed. We are being asked to believe that a county clerk (the job, not the person) should be able to pick and choose which items he or she (the person) feels would go against their personal religious beliefs. That even this person's signature on a document would constitute an religious violation.
If that is the true then where would it end? Would a morman clerk be allowed to refuse to issue any document that would allow a restaurant or bar to serve alcohol? What about a simple coffee shop? How about a Christian clerk refusing needed documents to open a jewish synagogue (they did kill Jesus, after all)? How supportive would this lady have been of a catholic clerk refusing to file any papers relating to a divorce?
People in her county would be held hostage to her personal interpretation of her personal religion.
The original issue being forced to do something contrary to her religious beliefs, how exactly is that analogy a red herring?
analogy
noun, plural analogies.
1.
a similarity between like features of two things, on which a comparison may be based:
the analogy between the heart and a pump.
2.
similarity or comparability:
I see no analogy between your problem and mine.
3.
Biology. an analogous relationship.
4.
Linguistics.
the process by which words or phrases are created or re-formed according to existing patterns in the language, as when shoon was re-formed as shoes, when -ize is added to nouns like winter to form verbs, or when a child says foots for feet.
a form resulting from such a process.
5.
Logic. a form of reasoning in which one thing is inferred to be similar to another thing in a certain respect, on the basis of the known similarity between the things in other respects
This