“People now say ‘I don’t even want to meet anybody who’s from the other party,’ even if it’s someone who’s perfect in every other way,” Ms. Adler says. In past election years, about a quarter of her clients wouldn’t date a member of the opposite party. Now it is three-quarters, Ms. Adler says. She has fewer problems matching Democrats and Republicans in Los Angeles, New York and Washington, but in swing states, “it’s 24/7,” she says.

Shelia Davis, who lives in the perennial dogfight that is Florida, ought to be a matchmaker’s dream. Petite with long blond hair and born in Tennessee, Ms. Davis is an ebullient entrepreneur whose executive-search firm and other interests have provided her with a comfortable retirement at age 47. Divorced and a mother of three, she is a world traveler, art lover, wine collector, dedicated philanthropist and a serious ballroom dancer. She is drawn to professional men, mostly CEOs, doctors and lawyers, but the artist in her longs for “someone I can play intellectual ping-pong with,” she says…

And there is one more thing: “I will only date a Republican—or a Democrat who has come to his senses and is now a Republican,” she says. “I believe in the free-market society that made America great. I don’t believe in Obamacare and government handouts. I want someone who’s a giver and not a taker.” She worries that for anyone with a liberal viewpoint, “it’s simply not possible.”