Even when faced with overwhelming evidence to the contrary, the conspiracist remained stubbornly ______, refusing to concede that his elaborate theories might be unfounded.

✓ Correct Answer: Option B

The phrase 'stubbornly refusing to concede' describes an unyielding nature. Both 'obdurate' and 'intransigent' mean stubbornly unwilling to change one's opinion or course of action, fitting the context.