One thing that I regularly hear in Hungary is how people are concerned that dialects are disappearing. No doubt with the rise of mass communications, dialects are becoming less frequent, an example of which is that what is commonly considered to be standard American English pronunciation is actually the Midwestern dialect. As a means of solving the loss of dialects in Hungarian, I think they should recognize the mispronunciations of Hungarians who grew up in the West as different dialects.
There’s the story (I’m guessing it’s true) that about a hundred years ago, a person from Budapest and a person from the southern Hungarian city of Szeged practically needed to write things down to communicate, as even though they spoke the same standardized language, the pronunciation was so different it was barely intelligible. When I speak Hungarian, it’s with an American accent, or as I jokingly say, I have a Californian dialect.
In the old days, I used to try and hide the fact that I was a külföldi, but these days I don’t really care anymore. Hell, after telling the locals I’m a külföldi, they stop treating me like I’m a special-needs case and understand why I’ll occasionally mispronounce something or reinvent Hungarian grammar mid-sentence. This also has the added benefit of clipboard-wielding people on the street leaving you alone.
Granted, I’d say my Hungarian is among the top 5% of Hungarians born and raised abroad, but even though I’ve lived for longer stretches in Hungary over the past five years, my accent, while improving, still remains. That’s why, if it was officially recognized as a dialect, I could get away with a lot of the stupid things I unintentionally say with a quick reply of “oh, that’s just how we say it out there,” even if I’m just completely bullshitting the person I’m speaking with.
I’d say the main thing that comes up is that when I’m not paying attention, I’ll say the letter R like I do in English, which in California is a very back of your throat sound, kind of like pirates, but not quite so pronounced. In Hungarian, conversely, R’s are rolled. Not as badly when you see someone trying to put on a fake Scottish accent, but they roll nonetheless.
Not only would this make it easier for fellow külföldis when they make the journey back to Hungary, but it would also see a resurgence of dialects in the Hungarian language. American-Hungarian already has its own slang which is primarily derived from Magyarized English and leaves the Hungarians in Hungary absolutely flummoxed, so what’s there to lose? If Texas German is an actual dialect, why not do the same with Hungarian?
While I’m at it, I’d also like to add a rule that accent marks in Californian-Hungarian are not mandatory, thus instantly improving my spelling 50%.

Do Hungarians have a concept of a stereotyped American-Hungarian accent? Do they pigeonhole you based on your accent, or just not know why you’re talking all weird?
There is a stereotyped “foreign” Japanese accent here, which no one I’ve ever met actually has, but even that stereotype would never be accepted as a legit dialect since it’s not perceived as Japanese in origin. In fact there’s very little recognition of dialects in the public sphere to begin with, so asking people to recognize non-native accents would be a huge leap.
If külföldis are as numerous as those NY parties years back would suggest, you might try entertaining this idea a bit more.