It doesn't come across as rude at all
@Lorcan - you asked very relevant questions in a very polite manner.
Only stupid people never ask questions
I actually live in Switzerland so although technically we are geographically in Europe, it isn't quite the same as living in Europe (if that makes sense).
The Swiss never joined the European Union for that very reason - they will do things their own way, and no one else will tell them differently.
So I can't really comment from a European perspective, but Coke here is most definitely vegan, but then Coke in Switzerland is actually made in Switzerland, so the ingredients will be sourced differently due to tighter controls and a smaller market (I don't imagine it is profitable for Coca Cola to export their Swiss Made Coke

).
View attachment 99963
I am not sure about the Oreo thing and we currently don't have any in the house (becasue quite frankly, vegan or not, they are not something I want to eat too often), but I will certainly check this next time I am in the supermarket.
I am fairly sure they are vegan here becasue I have a friend who is pretty strict about this sort of thing, and she recently bought them along to a coffee morning that we both attended. But I will let you know.