People from other countries think that the British are cold and unfriendly.
This isn't a statement about the character of the British. This is a statement about perception, about what other people think. The verb of the independent clause is "think". This statement happens to contain a subordinate clause with the verb "are".
In a tag question, the tag is another clause which attaches to an independent clause:
People from other countries think that the British are cold and unfriendly, don't they?
In your example, the verb of the main clause accepts do-support. The verb of the subordinate clause does not. In another statement, both verbs could accept do-support:
People from other countries think that the British hate coffee, don't they?
If the tag could apply to either the independent or the subordinate clause, this would be an ambiguous question: don't people think that? or don't the British hate coffee? Instead, the tag can only apply to the independent clause, and the only available interpretation is don't people think that?
We could ask a follow-up question about whether the British hate coffee, but that follow-up question would not be a tag:
People from other countries think that the British hate coffee. Do they?
The follow-up question here is an independent clause and a separate sentence. Since the tag would be "don't they", the natural follow-up is "Do they?". "Don't they?" is a grammatically possible follow-up, but it's too easy to mistake for a tag in this context.
We could even ask a follow-up question if the verb of the subordinate clause does not accept do-support:
People from other countries think that the British are cold and unfriendly. Aren't they?
Here, both "Are they?" and "Aren't they?" are reasonable follow-up questions, since neither one can be mistaken for the "do they" tag that could attach to the independent clause of the original statement.
The model in the test question is punctuated as a single sentence. You need to pick the answer that works as a tag, not as a separate follow-up question.