One suspect's file warned that she was "involved in puppet making and allows anarchists to utilize her property for meetings."

Puppets! I was always suspicious of that fucking Geppetto.
Here's the thing. As you know, much of what the police do when they infiltrate and investigate citizen groups is not a constitutional violation. There's a time when it may have violated regulations and a few statutes, but most such restrictions have fallen by the wayside post-9/11. Absent actual searches, wiretaps, or other intrusions, their infiltration of groups — accomplished through deceit, but still involving voluntary presence — does not breach the Bill of Rights.
But as your post suggests, there are still plenty of reasons to be unhappy about it. Among them:

1. Government classification of a person or group as terrorist can have both informal and formal legal ramifications down the road. Most judges will be more likely to give cops a search or arrest warrant if they are told that the suspect has been classified as a terrorist — even if that classification is entirely arbitrary and capricious. Plus, though confidential classification by the cops is not the same as open classification under statutory rules, it is a step in that direction. It is illegal to give material assistance to a group once the State Department has classified it as a terrorist group under 18 USC 2239B, for instance.

2. Tolerance of this nonsense is tolerance of shameful waste of government resources. Sending snoops to sit around the local hemp collective while they talk about what color to paint the giant paper mache turtle costumes this year not only flushes my tax dollars down the shitter, it allows the government to posture as if it’s doing something about the real threat of terrorism when it is not. Granted, it’s not like “Lucy” is likely to be shutting down any Al-Qaida cells any time soon if she’s re-tasked, but Jesus, can’t we make her learn Arabic and go translate web sites or something?

3. Tolerance of government investigation of peaceful and intractably harmless peaceniks and tree-huggers normalizes public tolerance of the invasion of people like Lucy and her pencil-pushing supervisors into every sort our business.