Can the police spy on us? Only if they have probable cause to believe that criminal behavior is taking place and a search warrant signed by a judge. Short of probable cause about the very persons on whom they are spying, not about a group to which those persons belong by birth or by choice, the police may not lawfully spy, and judges will not sign search warrants without specific probable cause about specific persons. The specificity is required by the language of the Fourth Amendment. That language also guarantees that quintessentially American right -- the right to be left alone -- by establishing articulable suspicion as the linchpin of all police pursuit of anyone for anything, and probable cause as the trigger for search warrants.
Can the police choose a target upon whom to spy based on the target's religion? No. The courts have been clear that under no circumstances may religion lawfully be the sole or even the principal basis for surveillance. That's how World War II got started: German police targeted Jews because they were Jews, and for no legitimate law enforcement purpose and without probable cause.
Was the New Brunswick operation criminal? Yes, it was. It's not too late to charge the NYPD officers or the CIA agent in state or federal court for spying. It's also not too late to charge the FBI agents and the New Brunswick cops in state or federal court for failing to obtain a search warrant (if they didn't have one), and for malfeasance in office by not arresting the spies.
The sacrifice of liberty for safety is illusory. The liberty lost does not return. The safety gained is not real. Who in New Jersey voluntarily gave up his liberty? Who can feel safe or free with government agents secretly and unlawfully monitoring them? What is the reliability and vitality of constitutional guarantees if those in whose hands we repose them actively violate them? What religious group might law enforcement target next? How dangerous to personal freedom is a cabal of law enforcement when it looks the other way to avoid prosecuting its own?