Deliberate offence
The tactic of taking deliberate offense is a common one in debates in politics and on the Internet. It consists of finding or creating an interpretation of an opponent's words that is repugnant in a racist, sexist, or otherwise inflammatory way, bypassing the actual topic of argument. This gives the "offended" party the automatic advantage of victimhood, and ensures that future replies must tread very carefully.
Like many rhetorical tactics, it can be difficult to discern deliberate offense. Sometimes a sentiment can be actually offensive ("I'm not saying that all black people are stupid, just that they're all thieves."), sometimes offense is being manufactured ("I can't believe you said that Margaret Thatcher is ugly! That's just a slur against all women!"), and sometimes the person is just being stupid ("wtf y u say that everyone in a synagogue is jewish.") More often than not, they're just being stupid.
On the Internet, this is a frequent tactic of concern trolls, who will contort an opponent's words into any possible position to find a way to make them offensive. It is also particularly frequent during discussions of affirmative action, with charges of racism thrown around by both proponents and opponents, and during discussions of Israel, where any criticism of the country is labeled anti-semitic.