Sometimes I must discuss a subject with someone who has an emotional, not necessarily reasonable, connection to a subject. How can one discuss a subject or convince a person who has an emotional attachment to the subject matter? This might be a school teacher, or an ex-wife, or a voter, or another person whose viewpoint is in fact important to the wellbeing of my own family. So I can not simply dismiss and ignore that person's influence.
I've tried connecting the subject to other subjects of emotion for the person - however I seem to lack the connection to emotions to understand which emotion is dominant and will affect the other. As emotion seems to be the basis for the nature of so many people's reality, has the philosophic community developed tools for including these people in discussions? My specific need is to know how to convince these people, however I'm specifically asking about the methods that philosophers use to understand and talk with these people in general. Considering that philosophy and rule of the people developed closely in time and geography, I would think that such methods and tools would have been a priority for early philosophers. However I find little information on the topic.
Some examples, not comprehensive nor relevant to any discussion I'm currently having:
A "naturalist" who has been told that some oil has "anti-bacterial properties" and thus prescribes it for everything, even though they do not understand that different bacteria are sensitive to different treatments (e.g. gram-negative vs gram-positive bacteria). Asking which bacteria have been shown to be sensitive to the oil is met with contempt - they feel that I am being condescending towards their field even though I ask with enthusiasm and interest.
People who "just feel" that vaccines cause autism, even though extensive studies have disproven any connection. For some reason "just feel" is a stronger motivator than are scientific studies. I've tried to show them optical illusions and other tricks for which "just feels" is proven invalid, however, this has absolutely no effect.
I was unsure if this question is on-topic for philosophy.SE, but according to the site rules, "logic — the nature of reasoning and inference" is on-topic and that is exactly my concern.