A spat between Sweden and Romania; a car with an insulting plates (when read in Romanian) caused the Swedish embassy to release this rather ambiguous statement:
The Embassy of Sweden in Romania would like to clarify that personalised car plates issued by the Swedish Transport Agency are valid for travelling in the European Union. Personalised car plates should always be accompanied by the official documents for both the original and personalised car plates [...]
– According to the Swedish Transport Agency, personalised car plates are valid to travel with, also outside the borders of Sweden.
– Owners of personalised car plates should bring the original plates, in order to have the possibility to change them in case the receiving country do not accept the personalised plate.
– Receiving countries decide what kind of vehicles that are allowed to travel in their countries. Swedish authorities can not influence what vehicles receiving countries allow on their roads.
So basically any EU country can refuse to accept the plates from another EU country? (Or is that refusal permitted only for personalized plates?) I'm guessing a single case of refusal might not violate any EU directives or laws (since Sweden didn't mention any), but is there something in them regarding the recognition of plates from other EU member states and acceptance of vehicles displaying them?
Otherwise one can imagine a nationalistic row in which one EU country decided to disallow all plates from another EU member. That would surely contravene something regarding free movement etc. But is there something more specific about car plates in EU laws or regulations with respect to their acceptance in other EU countries?
Wikipedia has an article on vehicle registration plates of Europe, but it doesn't say much beyond what the common format of the plates is. Based on that it might look like accepting another EU member's plates is entirely up to the host country. The Wikipedia page on the Vienna Convention on Road Traffic, which techincally is not EU law, but is mostly applied in EU does say
One of the main benefits of the convention for motorists is the obligation on signatory countries to recognize the legality of vehicles from other signatory countries.
But does this actually imply the right to circulate? Are there exceptions allowed?