A great deal of evidence is present in Toni Cade Bambara's short story "Blues Ain't No Mockingbird" to explain exactly why Granny is upset by the men filming her house and family with their camera.
One piece of evidence concerns the men's motive. As the men explain, they were sent by the county as "part of the food stamp campaign." In other words, the county is apparently voting on a decision as to whether or not to grant poor citizens in the county food stamps. The poor in the county would be the underprivileged African Americans, just like Granny and her family. Therefore, the men are apparently there filming Granny and her family to collect evidence for the campaign. However, the next statement made by one of the men is extremely telling:
I see you grow your own vegetables ... If more folks did that, see, there'd be no need--
The man breaks off his sentence, but it is very clear that he intended to say there would be no need for food stamps. In other words, the men are not there to collect evidence for the county to prove just how badly the underprivileged need food stamps; they are there to try and disprove that there is a need for food stamps, to probably disprove that the underprivileged exist at all.
Hence, in Granny's eyes, the men with their camera are mocking her and her family. Granny's interpretation of the men's behavior is clearly seen in the story she tells the children about once witnessing someone with a camera photographing a man in misery as he was about to jump off a bridge. In Granny's eyes, it's immoral to photograph living human beings in misery as if they were a sideshow. Therefore, Granny tries to run the men off her property and has Granddaddy destroy their camera.