Analyzing those answers, Dr. Broockman and Mr. Kalla found that the views of about one in 10 of the voters canvassed on transgender issues had shifted in favor of equal rights — by an average of about 10 points on one measure, called the “feelings thermometer.” Ten points on that scale is roughly the amount that the American public shifted in its views on gay rights between 1998 and 2012, a period when eight states legalized same-sex marriage.

And one in 10 voters, Dr. Lupia said, is larger than it may sound: “Any presidential candidate would welcome that kind of effect from a doorstep conversation.”

To test the resilience of the attitudes of the canvassed voters, the researchers showed each one an attack ad video used elsewhere to challenge transgender protections like Miami-Dade’s. Those ads hit their mark, immediately reducing voters’ support; but the effect was short-lived, and that support rebounded weeks later, the study found.

“The moment for me, when I knew we had something, was when we got the data back from the three-week survey, and found that the effects persisted completely and remained large,” said Dr. Broockman, as assistant professor in Stanford’s graduate school of business.

The researchers, however, had no way to test whether those changed attitudes would translate into altered votes.

The finding is a validation of the Los Angeles L.G.B.T. Center’s work, which it calls deep canvassing. The center had commissioned the first study in 2014 to see whether its door-to-door work to build support for gay marriage in Southern California was getting traction. That by itself made it a somewhat novel project, in that political activists rarely engage academic researchers to do controlled studies — or vice versa.