Undecided people are generally the most willing to really listen.
Once people begin down a path of having an opinion on something, it becomes harder to change their view. This is because of mechanisms in the brain that automatically activate when we make difficult choices, mechanisms that serve to resolve cognitive dissonance. As the abstract of this study states: "A choice between two similarly valued alternatives creates psychological tension (cognitive dissonance) that is reduced by a post-decisional reevaluation of the alternatives." In other words, when we see two options that both seem somewhat reasonable, but must choose only one, we experience cognitive dissonance. The brain kicks in to resolve this dissonance, creating positive associations with the choice we made and creating negative associations with the choice we rejected.
What happens when we encounter dissonance-generating information about the choice we now prefer, our brain once again tries to solve the dissonance, by becoming less responsive to information that doesn't conform to one's already held beliefs, with certain areas of our brain failing to activate when we encounter dissonance-inducing information (such as disagreement or facts that go against our position). To put it simply, we respond very actively and positively when something confirms our beliefs (resolving dissonance), and respond somewhat negatively or impassively when something contradicts our beliefs, or even double-down and tune out dissonant information, to a degree that is measurable on brain scans. (Here is a thread I made about this a while back.)
I am not an expert on psychology or neurology, I just decided recently to study up on experimental psychology and neurology regarding things like decision-making, confirmation bias, forming opinions, etc. and soon I want to do some study into what happens to people psychologically/neurologically while in cults, as well as other organizations such as religions or political parties. My reason for doing this is to become better at communicating with people who have really entrenched themselves in a certain stance and have a fact-repellant mechanism going on. So far the main thing I have seen mentioned alongside studies into this kind of thing, is that because people are more responsive at a neurological level, to agreement, it is a decent strategy to begin such arguments by agreeing with them in some way, and I imagine it's also a good strategy to give people room to deal with their cognitive dissonance as it is generally a subconscious mechanism that actually makes it measurably harder for them to respond to facts. However, I know from experience it's very hard to be patient enough to do this, especially when the person is being combative or holds a very bad position, so I understand simply not engaging with ideologically entrenched people and focusing more on undecided people (which is generally what I do, and I think it is worthwhile and effective for people to do so).
However I hope that in the future, through a scientific understanding, I can develop a strategy for reaching people who are not just the middle, "undecided" types but that can also reach toward more ideologically entrenched people when I do run into them and have the time and energy needed to deal with their dissonance response on a case-by-case basis.