The only way you can really pull this off convincingly is through humility. If you are to approach a person you disagree with with sympathy, you have to start with the notion that they are neither irrational, malevolent, or crazy, but rather a sincere and rational human being who has reached different conclusions from yourself.
This does not mean you give up your own views, but it does mean that you recognize that neither you nor they are infallible, that neither your reason nor theirs is certain, and that the specifics of experience, temperament, and even heritage color the evidence you see, the way you see it, the way you select it, and the way you interpret it.
There are certainly writers who are convinced that not only is their reason impeccable, they have so much insight that they can fully comprehend the mind of their adversaries and thus understand both the nature and the pathology of their views. While the pathology part is, of course, up for debate, I can say with assurance (having been on the other side of these debates) that they never get the part about understanding the nature of the other person's views right. They hear them only with their minds in refutation mode, never in appreciation mode. They refute only a pale imitation of the views they have neither the sympathy, patience, or humility to appreciate.
A polemicist can get by on arrogance alone. But a novelist needs both arrogance and humility. They need arrogance because no one would write with the kind of confidence and assurance that a good novel demands if they were not arrogant. But no one will write with the kind of sympathy for characters of every stripe that a novel requires if they do not also possess a profound humility. You cannot understand or describe a person justly if you only see them by looking down from above. You must see them from every angle. You must look up as well as down. A work of art is an expression of vision and you need arrogance to express and humility to see.
Of course, there is a large market for polemical novels. Such works tend not to outlive the period in which the views they express are fashionable, and they are despised by those who hold other view. But if you are an ideologue of a popular ideology, you can make good coin turning out such novels. You will be preaching to the choir, but a choir is an appreciative audience. Engage your reader in the spirit of polemic from the start and they will happily go along with any characterization of the opposition, no matter how garish or unjust.
But if you want to be something other than this, if you want to give an honest portrait of how people come to differing views and the consequences that follow from them, with a focus on the nature of the human experience, rather than a focus on hammering home your point, then you need to practice humility. But if you succeed, you may produce something that is read by people of all sides and long after the issues of the day have been forgotten.