This post got me thinking. Not about the validity of the argument, I think sometimes it is valid, other times it’s a smokescreen.
But what do we call it?
It invariably happens when a group of people sharing a similar trait are insulted for that trait: someone comes in and says “if you substitute the word ‘black’ instead of ______, you can see how offensive what you just said is.”
Sharpton’s Law, perhaps?
Political correctness?
I was thinking along the lines of Godwin’s Law.
And it’s not necessarily politically correct…it’s not always an accurate comparison of another person’s viewpoint.
I have actually seen this exchange elsewhere.
“I really hate people who leave their cellphones on in the movie theater”
“You asshole! I do that–if you were to change the ‘people who leave their cellphones on in the movie theater’ to “niggers,” nobody would let you get away with it!”
(not verbatim, but close enough)
In the main, it’s a strawman. The premise (that insulting people because of their weight is the same as insulting people because of their race) is incorrect from the get go. It shares baseline characteristics (a superficial trait is the basis for abuse) but that’s where it diverges, especially when it comes to obesity, which many perceive is something that only happens to lazy people who eat too much, and thus is controllable. (The same line of thinking is often used against gays, too.)
As for the phenomenon of that particular argument coming up – I’m not sure. It’s kind of a race card move, in a Godwin sort of way, but used instead against other prejudices instead. I like Sharpton’s Law, though I’m not quite sure it fits (unless he’s a Doper who has pulled this one. :D)
One formulation of Godwin’s Law is :
Describing the probability of the argument occurring.
As I understand your point, the issue is both the strawman effect — rephrasing another posters comments in an extreme way in an attempt to discredit them (possibly implied in Godwin’s Law) — and substituting black people as a group specifically and showing how another party’s comments regarding some other (non-racial?) group are akin to racism.
Maybe it could be called Blackjacking?
Sort of a hijack using black people…?
i call it obnoxious
I like it!
(even though we all know that hijacks use Cubans or Ay-rabs, not black people)
Interesting OP. I’ve wondered why it is on this message board, that a Pit rant can contain any measure of sexual, animal, and various other profanity laced epithets, and can be right on target, yet the inclusion of one of a dreaded few words or concepts makes the thread jump the tracks.
Like czechleslovakian, surprisingly
CzechOslovakian! 
false analogy, I’d say (assuming it is actually used in a false way).
If it’s used in a truthful way we could call it a true banalogy. 
And if they substitute a crescent-shaped yellow fruit, it could be a bananalogy