Every morning, Dan Kaplan finds an article next to his plate at the breakfast table, placed there by his wife, Sandy. It is always a jeremiad against Donald Trump.

Dan had done business with Trump and was impressed with his decisiveness. “Trump gets things done,” he said, and voted Republican for the first time in 2016. Sandy felt betrayed and outraged, hence her daily diet of articles, which never convince Dan.

Yet she persists. Why?

Mike Nelson is on the verge of alienating his beloved sister, Sheila, over his constant Facebook posts extolling Trump. He has already behaved so boorishly that his liberal brother and sister-in-law have unfriended him. “I was incredibly obnoxious about Obama,” he admitted.

Sheila is now the only family member who corresponds with him, because they were so close as children. Mike has cut himself off from those he cares most about, but he cannot control himself because, he explains, “Trump is everything.”

Even couples who vote the same way can have awful fights. Peter Collins and Jake Johnson are two Trump supporters in their 30s who have been together five years. But Jake idolizes Trump, while Peter, who supports his policies, disapproves of his character.

When they used to drink and talk politics — always a terrible idea — this otherwise rational and affectionate couple went berserk. On one occasion Peter ran from the room, yelling and slamming the door behind him, and broke a marble table when Jake pursued him. Jake reciprocated by smashing Peter’s cellphone into smithereens.

For my book “I Love You, But I Hate Your Politics,” I interviewed 50 people who were embroiled in unwinnable political fights with those they loved and sought my help in extricating themselves.

These disputes are ostensibly about political differences (what psychoanalysts call the “manifest content”). But, in fact, what is tearing these intimate relationships apart has a psychological basis (the “latent content”).

The failure to understand what lies beneath the surface prevents people from changing the way they interact.

Because politics has to a great extent replaced religion as a fundamental aspect of identity, serious disputes with someone important in your life can feel like abandonment and betrayal. The combatants then succumb to what I call “the conversion compulsion”: If somebody who must agree with you does not, you will try to change his or her mind by any means necessary. These means usually include raised voices, sarcasm and article-thrusting, and always culminate in repetitive mutual misery.

The people I interviewed badly wanted to improve their interactions. But this only becomes possible once the combatants accept that their conversion agenda is doomed.

Sometimes the way out is not to discuss politics at all, or to actively avoid particular issues, which was the solution for my conservative husband and me, a liberal, 39 years ago. But it only worked once I accepted that I could never convince him of the error of his ways on abortion or anything else because he didn’t think his ways were in error, and never would.

I discovered that it became possible actually to have a dialogue with him once I tried to understand his perspective and to offer mine in the same spirit: “Here’s my point of view on this. I want to hear yours.” But you have to mean it.

One couple, both Evangelical Christians from the far right and left of their faith although they belonged to the same congregation, made me feel optimistic.

Karen and Daniel Schwartz fought passionately over politics — immigration was their hot button — then figured out how to stop. Their secrets for success? No raised voices, no article-thrusting, no opening gambits like “How dare you think that!”

And, most important, recognizing the merits and exemplary character of their mates.

“Here’s our method,” Dan said. “We’ve learned more about ourselves. We’ve become confident enough that we don’t need to change each other’s mind. We trust one another.”

He summed it up. “People think that political agreement is more important than it really is in a relationship.”

To paraphrase Robert Frost, they “love the things [they] love for what they are.”

Jeanne Safer is a psychoanalyst in New York City.