Take the following premise. Bob sees Mike (who has blue hair) rob an orphanage, and considers him a bad man.
Bob exclaims in a public forum, “That blue-haired sneak! He should be found and put in jail.”
Mike (wearing a mask while on the run) highlights this statement, replaying a record of it in another location, and adding: “I can’t believe Bob would say such terrible things about blue-haired people! This is extreme bigotry!”
Jill, who also has blue hair, and Derek, who simply doesn’t like bigotry, both miss the context of the robbery that happened earlier, and are shocked at the isolated statement.
When the town meets later, the issue of a robbery at the orphanage is downplayed, and the town instead spends the meeting condemning Bob’s bigotry.

While a lot could be said about the whole sequence, I want to find out if there is a shortened term used to refer to the deception by Mike when deliberately misrepresenting the grouping of a targeted statement; eg, to build class solidarity the wrong way. The closest I’ve found might be “Strawmanning” or “Divide and Conquer” but it seems common enough I’d like to see if there’s a name.

I tried to generalize by picking “blue hair” for the example, but I admit it’d be an odd, off-color statement by race or appearance. There are still other forms of grouping that are more common to state in conversation, like “gamers” or “voters”, or “farmers”, in which such statements could apply to all, or just some, of that broad group.