Formal settings - and written conversation count as highly formal, as they cannot transport gesture & mimics - require more adherence to proper protocol, not less. As I said above, I vividly remember the first exchange that omitted the greetings & goodbyes years after the fact, and wondering what I'd done to offend the offender.
A complication I have encountered when using French on the internet, is offending some French people by being too formal. Learning French purely in a formal, classroom situation (and often only getting speaking practice addressing the teacher), I am much more at home in the formal "vous" form of French than the intimate "tu". Also, I was taught that prematurely attempting to tutoyer was just asking for a snub*, but some French internet people insist on it, even on first encounter. With my French being as bad and rusty as it is, half the time I can't remember the tu form of the verb. Culture is complicated...
*Par exemple:
"Peut-on se tutoyer?"
"Si vous voulez..."
That's a ways above my French, I have to admit. So take the following with truckloads of salt:
I would guess (!), based on German conventions about pronomial address, that it's not merely about familiarity/intimacy, but primarily about
rank. Those conventions were originally used at court, in order to express respect, as an acknowledgement of hierarchy. During the enlightenment, they increasingly became the default for any interaction (bit like Mr./Ms derive from Master/Mistress), but this didn't mean social rank and power-structures disappeared.
Usage varies with age (more importantly: differences in age), gender, difference in rank (esp in occupational hierarchies), there's probably a rural/urban divide, geographic variations, etc.etc. - and there's considerable confusion even amongst native speakers. Interaction with the Anglosphere also plays a role.
When I google 'Siezen' (the practise of using the 3rd person plural for formal address) in the Germanophone internet, I get tons of
current articles, each of whom will confidently express diametrically opposed stances on the appropriateness of using the formal or the intimate address e.g. in professional context. Some of my compatriots think that using the informal address in a working environment also fosters flat hierarchies and an egalitarian culture. Personally, I think that's an excellent way for people with direct, hierarchical power to keep their privilege on the one hand, without having to acknowledge it on the other. Just because your boss encourages you to use their given name doesn't mean you get to call the shots, does it?
German convention is that the intimate address is offered by the
higher-ranking person (not at all sure about the French conventions on social rank - my impression is that they're generally pretty serious about
l'egalité). When someone refuses your offer to switch to the intimate address, it could be a snub - that they refuse the offer of intimacy because they don't like you - or it could mean they see themselves as the higher-ranking and want to put you in your place. Or they might find it inappropriate, because there is a power-imbalance in play, and they want to keep their distance - I've done that with students I was grading, as a kind of warning:
"I'm not allowed to be your friend, and I have to grade you, and whether I like you or not mustn't make a difference". It could also mean they see
you as a the socially higher-ranking person, and feel uncomfortable about implicitly addressing you as an equal. Or, if they know you're a stranger to their culture, they might be unsure about conventions in
your culture and anxious about upsetting you - they could be trying to adapt to you. They could be making a mess of trying to adapt to you. They could be playing with clichés about their own culture - or yours. Etc.Etc. Then there's ways of transporting a message by deliberately subverting a convention - some of them a snub, others could even be a compliment.
Or ... tons of reasons for people to insist on a convention or not.