In other words, it does not matter if the policy is the same for all, and it doesn't matter if the policy is in compliance with the law? In the military, a commander who reacts to the enemy exactly as the enemy expects loses every time. In this case, the clerk set up a system to comply with the law that allowed her to also comply with her religious convictions.
But apparently complying in a manner not anticipated by the opposition is the same as non-compliance to some. I vehemently disagree (but try to avoid being disagreeable in such debates).
Yet, she needs a lawyer to defend it and the State of New York to priveledge it. That should tell you that there's something more going on than a simple policy change.
In this case, the clerk set up a system to comply with the law that allowed her to also comply with her religious convictions.
Really? Then tell me, what religious principle convicts her of engaging in sin if she processes this document.