If a law is clearly unConstitutional, you SHOULD not obey it. You are not obliged to obey an unconstitutional statute or edict of a court, no matter what the judge says. However, you may wind up paying the penalty or spending time in jail. This is the trappings of Tyranny and the small little steps of oppression creeping into our society.
This may not be popular sentiment on here, but, as much as an abomination to federalism and as much as the SCOTUS ignored the will of the people to take a stand via the ballot box with this terrible gay marriage decision, it is now the law of the land.
This clerk has zero discretion to ignore or disobey that decision. Her religious beliefs get checked at the door when she walks into work in the morning. She swore to uphold the Constitution of the United States. Again, as terrible as this decision was, denying gay marriage is unconstitutional.
The only ways to override that decision is via Constitutional Amendment or possibly an Act of Congress altering gay marriage in a way that moots the decision. It stinks, but realistically, it is what it is.