Yes, in German it’s a big deal, roughly the same as saying “Hey dude” instead of “Good morning Mr Smith”.
It's been changing for decades across a lot of languages. I grew up in Norway where these forms were dying out as I was a child (70's/80's) and mostly used to older people, to the point where they're now mostly used sarcastically to imply someone is a pompous ass or to very old people or in very formal situations. But go back another decade or two and it was common.
When I moved to the UK in 2000, even that was a weird shift up for me in formality (being called "sir" in shops, and having people actually use "mister" in front of my last name) compared to Norway.
But by the 90's my French and German teacher had both insisted we learn to use the formal forms but also both told stories about how that would already then sometimes make you seem old and stuffy, and to listen for what others said and if in doubt ask and to roughly assume we could get away with the informal form with our own age group and younger but default to the formal forms for older people just in case.
My own experience has been that most people I've met in Germany on business trips mostly have thought I've been more formal than necessary at first and told me I can use "du", because I've erred on the side of caution, but it's also varied a lot by location and age group and situation. Since I use my German relatively I'd rather start out too formal than misjudge the situation the other direction.
I have a good friend who spent half his childhood in Germany and then moved here (fluent in English, Deutsch, and Svenska). I asked about whether he would use formal or informal when visiting back home in Germany, or when talking to another German using German here in Sweden. Without hesitating, he said he always uses formal.
I have another German friend, who has been here only for about a year so far, of whom I asked the same: "Definitely I would use informal with any German here."
When I was in Germany, I could easily get away with using informal with anyone, because as clearly a foreigner with only moderate language skills, one can be forgiven many faux pas.
Interestingly, my spouse who is a fluent German speaker but also not native always falls into using formal address. She is quite often reprimanded for being too formal in situations that do not call for it. But that formal training was really rigorously applied, so she cannot help it. Even with our close friends sometimes.
W.r.t. my German-Swede friend, after we talked about it, he postulated that the reason he always defaults to formal is that he left Germany as a child, and so he never went through the transitory phase where children start to learn to talk to adults as equals.
I think the notion of using the formal forms only when talking to the royal family is close to how it would be in Norwegian too. In written language it retains every so slightly more use, but then too the only times it would be used non-sarcastically would be in something like e.g. an invite to something very formal. E.g. if I received an invite to a black tie event, then maybe it wouldn't be out of place. It'd still feel old fashioned, but then sometimes that is the goal.
> But that formal training was really rigorously applied, so she cannot help it. Even with our close friends sometimes.
I think that's the case for a lot of people who learned these languages some time ago - my teachers knew there was a transition happening, but would rather have us come across as too formal or polite than insult someone, especially as the focus was on learning these languages for business rather than for personal use, and it's really hard to get used to changing those things for languages you don't use every day in particular.
I'd say that sounds pretty similar to how it's used among German speakers, at least those who are 30 or younger.
I am saying, it was, because starting the late 90s with the spread of Internet and pseudo-anonimity all this just became outdated -- you had no idea whom you are talking to so observing the old rules were impossible. And those who have grown up with this simply didn't bother learning the rules. For me, when I was 18, it was a Big Deal that at our high school graduation party our class leader teacher allowed everyone to switch from formal to informal. It was basically the only time in my life when something like that happened, then I started using the 'Net shortly after (all this was in '93) and this stuff was just washed away.
I am in my late 20s and did find it excessive when university students from former Soviet Union (not knowing Polish well) use the polite form "pan"/"pani" for fellow students. I think there was some mis-mapping of forms. But otherwise it should be used in any situation when there is a hint of power imbalance or transactional relation. Informal to people at parties, formal to a store attendant and such. For example, I think that the fact that high school students are addressed by teachers with informal "ty", but are required to address them with "pan" is very demeaning and adds to the soul-warping, prison-like atmosphere of schools. At the university level, removing this felt like fresh air.
Recently there is a push in corporate/"hip" circles to use the informal way everywhere and even many young people don't like it. Many want to be able to hide behind "pan"/"pani" from your sales, marketing or otherwise pushy BS. I think that "ty" has to come with some expectation of sincerity and equality.
On the other hand, I find random French or German websites addressing their users with vous/Sie hilarious for some reason. It makes the relation seem businessy. Which okay, it often is in the modern internet.
With people my age I would probably always use the informal Du, but only in informal situations. In case of formal interactions, as part of a business transaction, etc. I would probably always go to the Sie if I didn't know the person and would expect the same in reverse. Anything else would probably be perceived as lacking respect. English doesn't have anything equivalent except maybe first name/last name basis, so it's always hard to explain to Americans.
Of course, as a foreigner things are always less strict and one gets some slack for not speaking the language perfectly.
For the most part, I find the use of mate as obnoxious at worst and awkward at best.
Maybe more comparable to addressing someone by their first name instead of Mr./Ms./Mrs. <last-name>.
Apart from that, people handle it differently. "Sie" basically always for people older than you and some use "du" for others around your age (unless it's in a more professional setting). There is no difference between the countryside and cities.
Sie!
Sie hast!
Sie Hast Mich!
I can vouch for the Kassiererinnen-Du being used. My mom runs the butcher in a supermarket. She and and many of her coworkers share a lot about themselves, but they still address each as other as Frau Schmidt and Herr Schulze.
Similar in Sweden 50 years ago.