I dont enjoy casting people into out-groups, but I understand its appeal and necessity for some people. However, I dont give BotD for the other persons benefit. I do it for my own peace of mind and because I find it yields better conversations overall. Sometimes conversations go nowhere, or people deliberately try to manipulate. Those conversations yield nothing, but that's okay. No one owes me anything, afterall. there's always the future.
I find the best way to keep people open to changing their minds about something either now or in the future is to make them feel like they are free to support whatever they want. Then I act as a source of information and act as a safe zone for thought-exploration.
People do not enjoy feeling hunted. and that goes for educated people hunting uneducated people in order to teach them something or else be out-casted. I think a response of "fuck you, go ahead and outcast me" to that would be pretty normal.
I would much prefer in-grouping people with proper differentiation. "so and so is a great cook!" instead of "so and so doesnt understand climate change and couldnt hold a rational conversation with me about it that one time so I dont associate with them anymore and if they die then good riddance". People want to be validated. Sometimes finding something to validate someone on rather than attack them on the points of disagreement can help reshape their identity. they might never agree with you, but maybe you can move them towards ignoring the topic entirely within their lives in favor of other things that are better aligned with the good of society.