Kim Davis has been likened to Rosa Parks, on the basis that she's breaking the law as an act of civil disobedience. The question of the aptness of the analogy is worth exploration. The problem is not that Kim Davis is breaking the law as an act of civil disobedience. The problem is that she's discriminating against people on the basis of her faith. She isn't making a moral argument.
A book written in the Bronze and Iron Ages sets forth a prohibition against a kind of conduct that may otherwise be natural. In the absence of any supporting evidence, people continue to assert that the book is the inerrant word of the Almighty. On that basis she discriminates against individuals who purport to love one another so much they want a contractual life commitment, one to the other. That's not a moral argument. That's just saying a rule from time immemorial prohibits a kind of conduct and accepting that as a principle of action without further justification.
A post-Enlightenment society with increasingly secular values and a somewhat rational outlook finds said discrimination to be outrageous and unacceptable. The clearinghouse for hearing all information and argument on the question and adjudicating the matter in a civil manner has set forth a holding, one which stands for the proposition that homosexuals have a protected right under the law to marry that cannot be abridged by the arbitrary whims of local officials on the basis of their provincial world views and belief systems.
If this conflict cannot be resolved by peaceable means because of Mrs. Davis' intransigence, she and her supporters will face consequences, namely state coercion or even violence, similarly-situated people who have had non-capricious reasons and principled positions have faced.
The essence of being an American is to be in such a state as to have an emotional attachment to the symbols of the country without actually understanding anything at all about their original meaning or historical significance. Comparison of Kim Davis to an iconic civil rights era personage, as well as the notion that the Constitution justifies arbitrary discrimination against particular sociological propositions because it's a document ensconced in Judeo-Christian values, reflects this kind of truly American fundamental misunderstanding of the history of American ideas.