For a large part of American history, suffrage for noncitizens in local elections was the rule, not the exception. From 1776 to 1926, 40 states allowed it in some form, at some point. When voting was restricted to white, male property owners, citizenship was not the central qualification.

But as millions of people from the southern and eastern regions of Europe — people whom, at the time, Americans did not universally regard as “white,” and whose political views were deemed suspect — flowed into the United States in the late 19th and early 20th centuries, anti-immigrant sentiment drove the country away from noncitizen voting, said Ron Hayduk, an associate professor of political science at San Francisco State University and an expert on noncitizen voting laws.

The repeal of these laws coincided with the enactment of other restrictions, like poll taxes, literacy tests and voter registration requirements. And the return of these laws in scattered municipalities has also coincided with a shift in the way immigrants are viewed.

Recent years have brought a sort of tug of war between more and fewer restrictions on voting. There seems to be a cluster of local efforts to allow noncitizen voting, Mr. Hayduk said — but at the same time, other officials are pursuing strict voter identification laws. And President Trump chose an advocate of those laws to lead the federal commission investigating voter fraud. The intensity of the debate about immigration has led to a bifurcated trend, with policies gaining traction in opposite directions.

Ms. Nagle, the sponsor of the College Park measure, said she understood why some people “feel that voting is a right tied to citizenship.” In fact, she said, she once felt that way, too.

But “about two years ago, someone mentioned that it didn’t seem right for students who are here for a short time to have the right to vote and residents who have lived here many years not have the ability to vote because they are not U.S. citizens,” she wrote in her email. “As I thought about it, I began to think, ‘Why wouldn’t we want our neighbors who live in this community to have the ability to vote?’”

The debate over noncitizen voting speaks to much larger disagreements about the place of immigrants in American society, Mr. Hayduk said.