It depends on how you deal with them.
The problem being that if this reporting person phones to say that this lady has taken a photo of this sticker and it causing them distress. The call taker tells them that its "not a police matter and goodbye" - end of story.
The reporting person then goes to the press and makes out that this lady is a serial terrorist who is terrorizing their community causing stress, harassment and anxiety. They told the police their concerns and the police did absolutely nothing.
The press get hold of this and make the police force look corrupt and not dealing with a potential huge incident properly.
Therefore, the force take the option of passing the job onto a cop to deal with. That way, if there is any fall out, the force can blame that one cop for not handling the job properly.
Vexatious complainers happen a lot and they are not easy to deal with. You can't just simply ignore them all the time as you end up with the 'cry wolf' scenario.