I guess the complaints are because the format is unfamiliar and strikes non-software people as being non-standard.

Perhaps use a format like 3/Nov/2021?

Can still be ambiguous because "list." means October in Croatian but November in Czech. Also, "lip." is July in Polish but June in Croatian and "srp." Is July in Croatian but August in Slovak.

Maybe it's just Croatian that's ruining it for everyone.

I'm guessing every language ruins something for everyone else.

Around this part of the world, almost everyone calls tea by some variation of the word "chai". But not us. In Polish, it's herbata!

That's missing the point of pressuring the other side to adopt ISO 8601.

(And in general case, of electronic documents with wider audience, using 3/Nov/2021 excludes people who don't know English (or the language in which you encoded the name of the month).)

The vast majority of documents are written in a language anyway so you can safely encode the date in it. Does any other language even have two different, conflicting date formats like that?

English is the only one with conflicting date formats I can think of (US vs UK), but in case of government and corporate documents, those are sometimes bilingual - with form labels in the primary language having a small-font translation to English below.

(Real use case: I recently sent a Polish equivalent of OSHA form to my line manager in UK, and I used a bilingual version. As you can imagine, I set the example by filling my part of the document using ISO 8601 for dates, so that once the document returns to the Polish corporate office, there won't be any possible confusions.)

No.

People were unfamiliar with showering and brushing their teeth. We move forward.