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That language can be a difficult barrier to overcome but probably in a much different way than you anticipate.
I manage a project team for an American company and about 90% of the customers my project managers (and therefore me) interact with on a daily basis are Swiss or Western Austrian. And I have a few Swiss colleagues too.
At first I was quite excited about the prospect of working with Swiss people because I happen to be fluent in Hochdeutsch (Standard German). However, you probably already know that most of Switzerland speaks a very specific dialect of German (Schweizerdeutsch / Swiss German), as well as French and Italian (and Romansh).
After a few months of daily interaction I was actually able to understand Swiss German about 99% of the time. There is some different vocabulary and grammar to Hochdeutsch but it’s doable. You can learn the quirky words with the help of the internet and I watched a lot of Swiss German news and radio.
I thought it would be a good idea to try starting to talk Swiss German back to people who spoke Swiss German to me. But that is actually not a good idea. I would say in 80% of cases Swiss people told me that they would prefer if they continue talking in Swiss German, and I talk in Hochdeutsch or we both switch to Hochdeutsch.
Sometimes I meet people who are fine with me attempting Swiss German but this is not the norm. However I have found that this quirk is unique to Deutschschweiz. I have never encountered a similar problem in French or Italian speaking Switzerland. I’m not fluent in French but understand it well enough, so in French Switzerland I would reply in English. In Italian speaking Switzerland people are actually extremely happy when you speak Italian with them, probably because they’re the smaller language community in CH.
I found that interesting and at the same time a kind of barrier to overcome. So if you move to Deutschschweiz (the German speaking part of Switzerland) you will probably be inclined to speak Hochdeutsch at first, as attempting Swiss German might not be well received by locals.
Nowadays I speak a kind of mix when interacting with Swiss people. Something like Hochdeutsch, but I usually use very Swiss specific words, like Velo instead of Fahrrad (bicycle) or Tram instead of Straßenbahn or Grüezi instead of Hallo. I guess my Hochdeutsch does have a distinct Swiss dialect by now because many German assume I’m Swiss when interacting with them but that’s subconscious and I don’t try to speak Swiss German on purpose.
As a french speaker : Swiss french has very few differences from standard french, except for counting (eg. 90 -> quatre-vingt-dix 🇫🇷, nonante 🇨🇭, yeah the swiss one makes way more sense), and some expressions or words like "tantôt" or "souper", it's the same.
That's why you haven't encountered this problem in Romandy. I don't know for Italian however.
You took French and made it better!