Most of the ladies in my French-language yoga class are French, but some of them are from the French-speaking part of Switzerland. To give you an idea of how close Swiss-French is to French-French, one of the Swiss ladies mistakenly thought that one of the other Swiss ladies was from France -- and this was after being in class together for several weeks, with plenty of conversation before and after class!
One of the Swiss ladies told me just a few weeks ago that she'd lived in Asia, but moving to the German-speaking part of Switzerland was a bigger challenge culturally (and was viewed as a bigger adventure by her friends and neighbors of the French-speaking region).
Here's another quick story to illustrate:
A friend of mine was waiting in a chaotic line, and since it wasn't moving, her husband took the children to wait somewhere else. Another lady immediately moved up to squeeze my friend out of line. When my friend indicated that she was still in line, told her she wasn't standing in line properly.
"Oh, and squeezing right up against each other is going to make it go faster," my friend replied.
"This is how we do it in Switzerland, and if you don't like it, you can just go back to wherever you came from," was the reply.
Note that this conversation actually took place in German (my friend's native language), and my friend never stated that she wasn't Swiss. Of course, she didn't have to.
[Then another lady (a lady my friend had assumed was German since she'd been speaking perfect high German earlier) suddenly switched to Swiss German to dispute the other Swiss lady's claim about "how we do things in Switzerland."]
Switzerland has an extremely high proportion of residents who are foreigners. According to this website I googled, foreigners account for more than 20% of the population. That's a lot. It would be nearly impossible to avoid tension between the foreigners and the native citizens.
However, I think the problem is exacerbated by having an official language (for all important business, official documents and instructions, etc.) that is not even mutually intelligible with the local dialect. It's like if you had to learn Italian for all formal communication, but the locals would all speak amongst themselves in French. Swiss German -- this so-called "dialect" of German -- is nearly that distant from High German.
If you don't believe me, take it from this Swiss comic book (Jetzt Kommt Später, by Kati Rickenbach):
The biggest problem with this, in my opinion, is the psychological distance it creates between the locals and the foreigners. The locals learn High German in school (essentially as a foreign language), and it's totally normal that they would prefer to speak their familiar native language. But there are huge barriers to learning Swiss German as a foreign language (it's not written, it's not consistent from one village to the next, it's hard to find materials and courses for learning it, especially if your command of German German is weak). So, effectively, the (German speaking) Swiss have their comfortable, familiar language for speaking amongst themselves, and then they have to switch to an uncomfortable, foreign language any time they want to communicate with a foreigner.
Communicating with foreigner becomes an annoyance, and even the most enlightened person is constantly making a mental distinction between "talking amongst ourselves" and "talking to them." It even contributes to a sentiment that Swiss people from other language regions of Switzerland are from a foreign culture.
German-speaking residents generally learn to understand Swiss German fairly quickly, but don't typically speak it -- so they are constantly marked as speaking the foreigner-speak. And I've heard credible arguments that the German-speaking Swiss feel more hostility towards Germans than towards any other (white) immigrant group.
Naturally, I intend to learn the local dialect. But the other weird thing is that a lot of Swiss people don't really want foreigners speaking their dialect. Many Swiss do -- there are plenty of people who feel that if you're in Switzerland, you should learn to speak like the Swiss. However, the particular dialect of Swiss German a person speaks is a strong marker of local identity. It's a way of telling people precisely where you're from. So trying to speak the dialect of some village that you're not really from sounds kind of weird and wrong to lot of people.
Personally, I think the solution is to stop the two-language system. Stop using High German** as the official language, and start using Swiss German as the official language of the Swiss-German-speaking part of Switzerland. Unfortunately, there's one big problem with that plan, illustrated here in a cartoon by Sergio J. Lievano:
The main reason Swiss German is considered a "dialect" (as opposed to being considered a separate language) is that it's not one language. It's a family of dialects that are (mostly, but not entirely) mutually intelligible amongst themselves. So it is impossible to agree on one official "Swiss German". It's so difficult that -- despite how fiercely the Swiss want to maintain their cultural independence from Germany -- it's simpler to just accept the foreign language rules from Germany than try and agree amongst themselves on defining Swiss.
[Aside: There was a humorous piece in the newspaper last week about how some Swiss people were up in arms over the fact that some foreign maps lumped together six different Cantons (the size of counties) as the "greater Zürich Area." Cantons that are outside of the Canton of Zürich -- can you believe it?! Meanwhile, plenty of people (my boss for example) commute into Zürich every day from neighboring cantons...]
However, I think it would be possible to agree to commission a committee of linguists from all over Switzerland to hammer out an official "Swiss German" language to serve as the official language (and just agree in advance to abide by what the committee comes up with).
If they created an official Swiss-German language, people could continue to speak the particular dialect of their home village. But people would also have the option of speaking a language that doesn't mark them as being from anywhere in particular -- and these two types of people would be able to communicate with each other in real time!
That's my humble proposal for improving inter-community relations in Switzerland.
**Technically the Swiss use a special version of High German, called "Schriftdeutsch" (i.e. "written German"), but it is nearly the same as the standard German language of Germany.