They came out originally saying that this team would be designed and trained to deal with terrorism and protests. They didn't offer a contrarian statement until the backlash.
So, this wasn't a situation where they realized they misspoke. This is a situation where the realized that what they planned was truly offensive to the people they "serve" and then re-adjusted their statement to placate them.
But, for the moment lets take them at their word. How often does New York experience terrorism? IDK, I would expect not very often under what is generally accepted by the populace to be considered a terrorist event. So, for the NYPD and the NY politicians to create a special group of officers to deal with these threats they're going to expand what they consider to be terrorism to a much wider range of criminal and civil activities.
If you look at the wording of the Patriot Act, it states, in part, that domestic terrorism is any act that attempts to change government policy through "intimidation and/or coercion". What is a protest? Is it a gathering of citizens to have their voices heard? No. That is called an election. A protest is something different. If I were an authority I could define it as coercion because it costs my administration money to deal with. The costs come in the form of extra, unplanned, policing and clean up. Any protest that devolves into violence will cross the line into intimidation.
But, you might ask, "what about peaceful protests?", to which I say, "What peaceful protests?". No protest the administration doesn't want to deal with, and that's all of them, is going to be peaceful when they will inject police instigators into the crowd. This tactic has been seen in Canada during the G20 summit, I think it was. The police were directly involved with inciting the protests to violence. And when they couldn't incite the protestors to commit acts of violence, they themselves caused the acts of violence which then justified the police forces standing in wait to move in and arrest peaceful protestors.