If the state of New York pursued criminal charges then all they could do is defend themselves in court. If they lose then they could appeal and if it passes in appellate court then they could have grounds to sue for 1st amendment violations. New York should see this as a worthy cause to test 1st Amendment rights. The 1st Amendment doesn't cover everything.
There is precedent in law, even in the religious aspects, that would have grounds and a basis in a suit against them. There are also many laws in place that serve as exceptions to freedom of speech. Slander/defamation of character/yelling fire etc. There is more than enough to ban the practice in the state of New York and also in the Federal Government.
Lawsuit filed over two years ago. Article states ruling was put on hold due to lower court ruling.
Lawsuit was about parental consent and if it is still in effect I'm going with the govt won but obviously the practice is still in effect. I'm not seeing any other articles about injunctions or appeals currently.
New York, Orthodox Jews Clash Over Circumcision
http://www.npr.org/2012/12/03/166399479/new-york-orthodox-jews-clash-over-circumcision