I’ve lived in Alabama my entire life. However, since I’m not an uneducated idiot, I realize that the Australians and British refer to all Americans as “Yanks” so it wouldn’t bother me. 
If a Brit or Aussie called me a Yank is a friendly and jovial way, I’d take it as such. It’s not a deadly insult or anything, it’s just one of those charming things Brits and Aussies say in their charming accents. The first time an Aussie told me I was a nice fellow for a Seppo, I had no idea what she was talking about but still found it strangely endearing.
The appropriate response is: “yank this”.
Hmm, well maybe I won’t lead with it for the ladies…
Thanks for the replies, very informative!
It depends where you are, too. If you were in the US, in the South, *maybe *someone would take you to mean a northerner, if they were not too bright.
If the conversation took place in Great Britain, or on the continent, you’d never get in trouble because the context is so obvious.
It also matters who’s calling us Yankees. You, Canucks, Murphs, Kiwis and Ossies can get away with it for sure. Anyone we personally know can call us a Yankee. Hearing it upon introduction to someone from somewhere else would be rude. And Yankees always have guns.
Followed by dropping of britches.
Just grab your crotch Michael Jackson style.
I had a father in law once who went by the nickname “Yank” (it was a play on his last name).
After I got past being mistaken for him, I’d listen for some manner of commonwealth accent in the OP’s voice and realize I was being called out as an American. Then I’d listen for the tone and try & decide if the query was hostile or otherwise and try to respond appropriately. Intent is much more relevant than the word. As for say, an English stranger approaching me with “Yank,” I might find it a bit odd me being a 'Merican was noteworthy enough to make it into the greeting, but I would not otherwise consider it derogatory.
FWIW, I don’t much care if a Deep Southerner calls me a Yankee–if that happens I might correct them and ask they refer to me instead as an abolitionist and we’ll see how the conversation goes from there.
They will then refer to you as a “damn yankee”.
For the record, Canadians never say “yank.” We may call you a lot of things, but yank isn’t one of them.
Well, we call you America’s hat.
It should be noted that “yankee” and “mother” are only half words. 
“Yank” coupled with an appropriate accent wouldn’t offend. Without the accent it might be troublesome.
Wait, bup! I received a memo this morning, and we aren’t supposed to refer to them as “America’s Hat” anymore. Instead, they are now to be referred to as “Our 51st State”.
In the future, check your inbox prior to posting. :dubious:
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And in answer to the OP, I would assume you meant “Hello” and respond accordingly.
I’m a Northerner (Ohio, specifically), and consider the American usage to always mean “Northerner”. If someone called me a “Yankee”, I wouldn’t consider it at all inaccurate. I wouldn’t generally use the term to describe myself, but that’s mostly just because I seldom find the topic relevant. I certainly don’t consider the term restricted to New England (and it would be absurd to do so, given that New York has if anything a greater claim to the term than New England does).
In the non-American context, I understand “Yankee” to be synonymous with “American”. Again, I see no inaccuracy, though of course a Southerner might disagree.
I’ve lived in Chicago all my life.
I went on a tour of the Jack Daniel’s distillery (great tour, BTW) and the tour guide* called me a Yankee. I told him I was a Cubs fan.
If someone from outside the U.S. called me a “Yank” I wouldn’t care one bit.
*This tour guide was as stereotypical as you get. Denim overalls with a white t-shirt, straw hat and missing teeth.
Incidentally, if one of you yanks replied “Not bad, limey” how should I take that? Should I consider it derogatory? Say that I’m not actually a sailor?
I’ve always understood Yank to be easier (and more accurate–the South lost, they are US citizens just like me whether they like it or not) to say than American. So it’s fine.
I’ve always understood Limey to be a mild pejorative on par with Guido or Squarehead. If we’re not buddies, I won’t call you Limey without expecting a fisticuff scuffle to ensue, or stinkeye at the very least.
In the South, we are American citizens. We are NOT yankees. Bless your heart.
I don’t think Americans have any particular pejoratives for Brits, Aussies or Kiwis, unless we add “goat f*cking” to the front of it.
That’s precisely the kind of thing I do say to my European friends who call me a Yankee. It seems to me to be just about exactly as insulting as “Yankee”; that is, not very. It’s a mild pushback to indicate that I note your mild cheekiness and return it without seeking to escalate. If this were poker, calling you a “limey” would be calling in response to your raise, rather than raising it further. That said, I am not a Southerner, though I have lived there. If you call a Southerner “Yankee”, they might take greater offense. It’d be comparable to calling a Welshman “English”.