I found the link to be very poor in details. The study itself is available here: https://www.journals.uchicago.edu/doi/10.1086/735630. It seems to be behind a paywall though. If someone has the pdf/link to a non paywall, please provide it.

The most important paragraphs from the link OP provided are these:

The results showed the most successful persuaders bridged identity divides, were able to view another person’s perspective and utilized personal narratives and the highlighting of common ground.

“What matters is meeting people where they are. Persuasion is most likely when the would-be persuader can see the issue through the other person’s eyes,” Naunov said. “The most effective arguments bridge identity divides through personal narratives and a respectful acknowledgment of the recipient’s perspective, which lowers defensiveness and increases openness to the persuader’s viewpoint.”

The least successful approach, the researchers found, was when would-be persuaders emphasized their political knowledge and engagement, traits that can be seen as off-putting and lead to negative results. Similarly, bombarding people with facts to prove them wrong was not effective.

“We tend to feel less hostility toward out-party citizens than out-party elites. Unlike political elites, ordinary citizens aren’t running for office, they’re not paid to advance a partisan narrative, and their careers don’t depend on toeing the party line. This makes them come across as more authentic, less strategic and ultimately more persuasive,” Naunov said.

Importantly, the study also raises big questions about the kind of divisiveness that is so common in the public space and social media platforms.

“However aspiring authoritarians and techno-feudalists might benefit from this kind of divisiveness, ordinary people do not,” said Naunov. “On a practical level, we should be asking what specific platform features shape whether people can even attempt persuasion in the first place. And how can we create alternative spaces that encourage more respectful and constructive political engagement?”

Perhaps a good framework for this sort of rhetoric is Marshall's Non-Violent Communication (NVC).