There is whole book devoted to how to talk to brexiteers, written in August 2019, but the methods have not changed.
Some words from the author, Peter Cook:
“A brexorcism needs skill, patience and time. Skills include gaining rapport with people you have little or nothing in common with, using a wide range of interventions from Socratic questioning, intensive active listening through to confrontation and catharsis. Patience is needed as I estimate a minimum of one hour maybe spread across several sessions to achieve meaningful mindshift. This also includes what counsellors call UPR (unconditional positive regard), even if you may feel that your target has no idea what they are talking about. This can be tough. The book has dozens of illustrative stories to help you keep going.”
· Do adopt the positive hallucination that your target is willing and able to change.
· Do listen avidly. Summarise occasionally so that you maintain rapport.
· Listen before attempting to challenge viewpoints. Sometimes the “story” is convoluted and takes a lot of time and patience to hear.
· Don’t judge your target. If you have got them to explain their viewpoint, let them tell you their story.
· Don’t befuddle them with facts unless they are operating inside the world of facts. A brexorcism is mostly about identity and beliefs change.
· Don’t give up after an initial encounter. Much of my most successful work has taken place over an extended period.