skye said:
I don't think it's that strict any more (and I wonder if it ever was).
Of course it's not strict. If it was, people would be using the two words in question accordingly. But instead, the majority isn't even aware of the difference, let alone pay any attention to it when using the words.
skye said:
I know there is/was some tendency to use Slovene as a noun and Slovenian as an adjective,
I still think the two cannot be used indistinctly. While people are using Slovenian as both, noun and adjective, it still sounds strange (at least to my ears) to use Slovene as an adjective, e.g. 'This is my Slovene friend.'
skye said:
but I don't think that anyone would consider it wrong if you didn't follow this rule.
I think people dealing professionally with English might complain. Specially if the 'reverse' usage appeared 'publicly' – that is in different publications, posters, signs etc. I have once come across a sign on the door of one of the classrooms of the Faculty of Arts in Ljubljana that said: “SUMMER COURSES OF SLOVENIAN”. The sign received rather merciless criticism among future translator (i.e. students of translation). Of course, they corrected it using a thick red marker and added (a rather emotional) comment – I don't remember exactly the words, but it was something like: 'Why are there studies of translation if everyone thinks (s)he can do it (better).'
skye said:
Just ask the native speakers how they feel about this. You'll see that most of them won't be aware of any such rule.
I don't think native speakers merit special attention here. A whole lot (if not even most) of them wouldn't even know where Slovenia is. And as in 99% of the cases the geographical adjective and the name of the language coincide (with such exceptions as Switzerland, Austria, etc.) who would suspect that this (incredibly) small Slovenia is the exception (that proves the rule).

And as long as we're inviting foreign students to “Courses of Slovenian” there's not much chance of them even noticing the other word, not to mention start thinking about its usage. It's like asking a Slovene how the inhabitant of Guatemala or Puerto Rico is called in his mother tongue ... Sometimes even a native speaker has to check a dictionary.
