Trying to understand your neighbor or anyone else doesn't mean agreeing with them, it means allowing them to be, to exist. Living in a civilized nation kind cuts the options down, you can kill them or let them exist and the civilized part takes care of the killing. People are going to be there and they're going to be how they are. That part about being how they are means an entire gamut from near saintly to impossibly pig headed. Yes, we do isolate or kill criminals.
A social society doesn't practice shunning, cutting people off from all discourse will create some really angry people or suicidally despondent ones. The upshot of not shunning people is that they will continue to write and say things that can put your teeth on edge and even sometimes educate you. Whatever their point you have to deal with them and one of the most practical tools we use is politics. It is a practical tool, not an idealized tool. It isn't much good at getting one out of many, it is fairly good at getting something done in the face of the many's competing interests.
There is little you'll get a clear majority to enthusiastically agree on as a policy without flat out scaring them out of their wits. Fear is a wonderful short term uniter, but long term it faces fatal drawbacks, an obvious one being its lack of substantiation or confirmation. If it is born out in facts - you didn't protect us and if it doesn't happen it isn't a problem. The best approach is to assume that no matter how good your idea or cause, it just won't sell without some help. If you happen to be in a known situation where you are short of support you need to know why.
This is the part about understanding your neighbors. They hold a stance or point of view that for them is entirely reasonable. It is not enough to
know that they are wrong, it is all about the process of being wrong. How do they come to be in that position holds the answers of what to do about that. There are the egregiously wrong, the wrong until the universe dies and ten minutes after and there isn't a damn thing to do about them. While these folks are in actuality few and far between, they are in sufficient numbers to create a base for a movement. Even if you cannot do anything about them, you can learn quite a bit from them. The importance is that whatever position it is that you are trying to overcome takes much of its cues from that group.
If you are trying to get the population to go along with something you have already made the assumption that the population is reachable. That means your problem isn't that their opinion exists it is in how to reach them and bring them onto your side of the proposition. Whether a person's point of view is rational or not isn't the question, it was reached through some sort of reasoning process and that is where the line of attack lies. If you do not understand how they got there, you have no ability to modify their stance of opposition.
The methodology of modifying that stance is extremely wide in a political endeavor, it may involve modifying your proposition and trying for incremental progress or it may involve education or it may involve flat out propaganda or... The approach or approaches are going to depend a great deal on the nature of opposition. You won't know any of that if you remain ignorant of the opposition. No amount of name calling or other denigration will educate you or put you in a position to deal with them. It makes no difference what the issue is, if it is divisive it simply is that. That division must be dealt with and unless you know why it exists you are reduced to name calling.
This isn't an exercise in morality or rightness, it is a simple fact that people as disparate as Adolf Hitler and Franklin Roosevelt managed it and achieved the ends they sought. They understood who it was they were trying to reach and how to do it. The word politics gets ugly connotations because the tools in use aren't shiny idealism. The idealists on both sides of the proposition are offended, compromises are struck, sweeteners are ladled on, and points of view get respected as having a basis to exist. There is no such discrete individual as a pragmatic politician, the word politician has already expressed the fact of pragmatism.
As soon as you enter the political arena you have accepted the proposition of pragmatism as approach. From that point on it is a matter of using it effectively and to do so you have to know who you are approaching and why they believe as they do. The point is to stop their opposition, to gain their permission to move ahead. The problem with taking an unethical or divisive approach to that isn't that it won't work, it is that angry, divided, and fearful people will turn on you with fury at some point - because that is what you've given them to work with or someone may offer them relief from a tiring exercise.
It is nice to right or good, but if the matter is of import what counts is moving in that direction to get there. In order to do that you need to win and the tools for winning are the levers that will move people into your position. It is a lot easier to get to those levers if you grant them respect as you attempt to learn them and that does mean understanding your neighbors. They are your neighbors, not strange aliens from another universe. Every one of us that has a relatively successful relationship already
knows this because the other person isn't me, we just forget the second politics enters the conversation.