Personally, I think many non-British people shouldn't have a hard time understanding that Northern Ireland isn't a separate country from Great Britain.
The French, Portuguese and Spanish all have territories that spans varying distances of water. Indonesia, Malaysia and the USA are three more examples.
Even British people shouldn't struggle with this as Shetland is 390 miles away from Great Britain. Northern Ireland, in contrast, is just 13 miles away at the closest point to Scotland.
I think non-British also should be familiar enough to understand that how many time zones a country has is related to how big its territory is. The entire British Isles is tiny really, so has one time zone. Russia, Canada and the USA are one of the biggest countries in the world, so have more than one time zones.
Although we're tiny, it's clear that England, Scotland, Wales, Northern Ireland and the Republic of Ireland all have an outsized influence on the rest of the world. Equally true is they all have complicated histories which is largely a result of living so close together. And yet we all have a history of working together for the greater good. This history is rarely acknowledged these days, I don't think.
Sad.
But I will agree with you that it doesn't make it right to call people thick over this kind of thing. I believe most people really don't think about their national territory too much as they take it for granted. Those in contested places clearly obsess, I would say, about it.