Opponents of same-sex marriage who saw the legislation signed into law over the weekend are worried the religious exemptions that allow groups to opt out of holding gay weddings aren't extensive enough.
"There are profound consequences for re-defining marriage," said Brian Brown of the National Organization for Marriage, which has pledged to overturn the law. "And this religious liberty exemption in my view does relatively little or nothing to protect such organizations and individuals."
Rabbi Avi Shafran of the Jewish organization Agudath Israel, said he was concerned about denying same-sex employees health care benefits for their partners.
"If we were to stand on our religious principles, which we would do, and not extend benefits because we don't recognize the union as a marriage, then the state could say that funds ... would be denied us because we are not subscribing to what the state considers to be proper marriages," Shafran said.
He said he was also concerned that businesses such as wedding caterers or florists would be sued because they didn't want to provide service to a gay or lesbian couple.
"Why should individuals be less entitled to religious liberty than organizations?" Shafran asked. "That's the logical problem here -- that what was given to organizations was not given to individuals, and there's no logical reason why that should be the case."
In the case of health care benefits, Donna Lieberman, Executive Director of the New York Civil Liberties Union, said the Marriage Equality Act is irrelevant.
"It has absolutely nothing to do with things like health care benefits and employment discrimination," she said. "That's a matter for the human rights law, the public discrimination law."
As for a scenario in which a business person wanted to avoid working for a same-sex wedding, she suggested Shafran and Brown were correct in their assumptions.
"If you're a wedding caterer, florist, whatever, you can't pick and choose who your customers are based on the color of their skin, their religion, their national origin, or the fact that they're lesbian, gay, transgender, bisexual, or who they're marrying."