David C. Kimball, a political scientist at the University of Missouri-St. Louis who has studied voting patterns in the county that includes Ferguson, said some other suburbs that became black majority communities earlier than Ferguson, such as nearby Dellwood, have since begun electing black leaders. “There is often a lag time,” he said, noting that Ferguson’s black population was only slightly higher than half the total as recently as 2000.

There are small indications, Mr. Kimball suggested, that black voters in Ferguson had begun to exert at least some political muscle even before Mr. Brown’s death. In a school board election for a district that includes Ferguson residents, three black candidates ran this year, after the removal of a popular black school superintendent. Only one of the three won a seat, but Mr. Kimball said he viewed the campaign as a modest sign of shifting.

Among some Republicans, the mounting political efforts have provoked tension. Told of the voter-registration booth that had appeared near a memorial for Mr. Brown, Matt Wills, the executive director of the state Republican Party, voiced outrage in an interview with Breitbart News. “If that’s not fanning the political flames, I don’t know what is,” Mr. Wills was quoted as saying. “I think it’s not only disgusting but completely inappropriate.”

Other state Republican leaders have distanced themselves from those remarks, and Mr. Wills did not return requests for an interview. “I think he spoke inartfully about one effort,” Ed Martin, chairman of the Missouri Republican Party, said in an interview. “Anything we can do to get more participation is good for all of us.”

Timothy Jones, a Republican who is the speaker of the State House, said any efforts to engage more voters in the political process were a positive development. “If people are lawfully registering people to vote, I have no issue with that at all,” he said.

Democrats, though, said Republican leaders, who control both chambers of the legislature in Jefferson City but not the governor’s office, had a long history of attempting to draw limits on voting that would most affect voting patterns among minorities in St. Louis, Kansas City and places like Ferguson.

“Their record is not about trying to open up the voting process but rather to limit it,” Senator McCaskill said in an interview. She said at another point, “It’s hard for me to believe that they’re sincere since they have blocked every effort for an early-voter law, they’ve put a pretend early-voting bill up where it really doesn’t allow for early voting, they have pushed, all over this country, for voter ID.”