The only people who have a justification for being upset about this are the people who want their religious beliefs imposed through government and law.
In no state where gay marriage, civil unions, or domestic partnerships are allowed are churches or other religious institutions forced to perform or condone these arrangements.. and this law for NY doesn't change that.
This is about government's role in marriage, not religion's. If government is to have a role in marriage at all (which I'm of the belief that it shouldn't) then its role must be in service of all citizens, not just those of one sexual orientation.
The only conservative justification for any government role in marriage is to recognize and incentivize beneficial relationships.
If you don't think a monogamous relationship.. of either the homo- or hetero-sexual variety.. is beneficial to society, you're an idiot.