Many years ago. Ansett Airlines of Australia introduced a policy where a first officer or captain could choose not to fly with a particular individual. If crewing discovered that several pilots had entered bids not to crew with one particular captain or F/O, this crew member would be invited into the management office for a please explain why so many had opted not to be crewed with this individual. In other words, everyone can't be wrong and for the situation to become that obvious that it was affecting rostering, the individual needs to be closely looked at.
This remained a successful policy and the people concerned soon got the message and usually changed their ways. The complaints were sometimes aimed at check pilots autocratic manner or for instance continued rudeness or sarcasm. At the worse the pilot concerned would be removed from check pilot duties. This policy was a good safety valve.
The suggestion of writing up a report on each flight at the end of the day, by each other on each other, is fraught with opening up a deep resentment and there is nothing more contrary to flight safety than two crew regarding each other with deep suspicion as soon as they settle into their seats. Leave those sort of personal evaluations to the experts - psychologists, not untrained pilots