Here is the whole thing in a nutshell.
Person A and Person B are both adult human beings and citizens who are not related to each other* and are both allowed to marry another person who is also an adult human being, a citizen who is allowed to be willingly married.
The only objection *possible* to Person A marrying Person B has to be religious. And you can't use religion to make law in the USA. That's how it's supposed to work, and if it's working otherwise then it's a violation of the Separation of Church and State.
Way to go, New York!
*State laws vary when it comes to marrying a relative, such as a cousin. (Probably because of possible birth defects in their children, or some other trumped-up reason for the law, because nobody actually forbids unrelated bio-parents from passing along genetic disorders if they choose to risk it. Something tells me that if two cousins, one of which has been sterilized, wanted to marry in a state where cousins are not allowed to marry, that no exemption would be made for them. I don't know that for sure, though.)