The New York Times suggested as far back as the Bush years—2005—that political persuasion was dead. Bu 10 years later they published one of the best summaries of current thinking on the topic, which defined "moral reframing" as the key element of successful political persuasion. For example, the most important thing to know if you're trying to persuade someone: let them talk about their values, then communicate using their language.
To do it, you have to get into the heads of the people you’d like to persuade, think about what they care about and make arguments that embrace their principles. If you can do that, it will show that you view those with whom you disagree not as enemies, but as people whose values are worth your consideration.