I understand psychological continuity as view that only preservation of psyche is important in determining if somebody survived or not. Like if my body, including the brain, is gradually replaced by robotic parts one by one, will I survive in the end, when the whole body will be replaced by robotic parts? Psychological continuity says "yes" if my psyche survive said body transformation.
Holding such view in the mind, let's take on another problem. Suppose Ivan is a zealous (Soviet-style) communist. Communism-related beliefs became integral part of his personality and consequently, his life. His best friends are zealous communists like him, he takes part in protests, volunteers and donates money for communist cause, votes for communists.
Now suppose he decided to challenge his communist beliefs. He started reading books that try to debunk said beliefs. And he found out said books completely destroyed all his communist beliefs. He then started reading books on views that were in opposition with his previously held beliefs. Out of several alternatives he was mostly convinced by ones that were promoting ideas of Anarcho-capitalism, with unregulated Free Market and unfettered capitalism, with abolition of the State and replacement of all State services, like law enforcement, with private agents.
Can we say, that from the point of view of psychological continuity, Ivan commited suicide? Communist beliefs were supposedly integral part of Ivan's character. But they aren't just no more, Ivan believes completely opposite things from now on.