On those rare occasions where logic changes minds, why does THAT happen?

This will only happen when the individual undergoing the change was not believing strongly in the faulty position, and this is another way of describing a situation when a part of the mind was carrying the negative prejudiced belief, but not the totality of the being. So when confronted, there was a sufficient portion of the mind not carrying that belief and it could be marshaled to, in effect, oppose the self and outvote that portion carrying the prejudice. This is not at all uncommon because the differing levels of the mind will develop differing beliefs and even within the same level of the mind, particular circumstances will cause beliefs to form and be added to the mix that are in opposition to other beliefs already present. This creates many complications and this is how people can struggle with themselves, first feeling one way and then feeling another. It is their reaction by turns in tuning into conflicting beliefs within their being—one for and one against something. So when beliefs are overturned through logic and reason, it is because the person is not so far out of alignment in terms of their total being or at least enough of their being to be in charge. Sometimes people will respond positively to such persuasion but then revert back to a prior position of prejudice when the pressure is lifted—when an opponent questioning their attitudes goes away. So there are as many potential scenarios as there are shades of meaning and belief within people from the many experiences of their lifetime and the cultural influences as well as karmic predispositions acting as powerful influences on what is accepted and what may not be informing beliefs as they accumulate life experience.