This is what confuses me. NYPD subpoenaed Twitter. Twitter said "no".
I don't understand why Rabbi Copwatch would be involved in fighting the subpoena.
Rabbi Copwatch should sue NYPD for infringing his civil rights by spying on him.
He has nothing to defend against. Under current law, if he doesn't want NYPD siezing papers and effects about him from Twitter, that is not his papers and effects, he needs to stop giving copies of data about himself to Twitter.
I don't like that law, but I think that's where the law sits today.
My understanding is that the customer of a service (like Twitter or an ISP) can sometimes file a motion to quash a subpoena given to their service provider. It depends on the jurisdiction and the nature of the case, however.
All court orders are warrants. That is the most basic definition of a warrant. So a subpoena issued by the court is warranted. A subpoena not issued by a court but accompanied by a separate warrant for the same information constitutes a warranted search or seizure where failure to comply with said search/seizure by the warranted party (ie. law enforcement) could constitute multiple crimes depending on the circumstances.
The third-party doctrine muddies this under current law.