Which of these sentences is correct?
Are they apples or they are bananas?
Are they apples or are they bananas?
When asking a question in English, the verb gets placed before the subject. So, "are they" begins a question, whereas "they are" begins a statement (declarative).
The second option is correct, but it could even be simplified to
Are they apples or bananas?
without any loss of meaning.
The second. You maintain the same structure in both parts.