“Nope, not at all. I have no concern whatsoever about it,” said Diane Wonchoba, an independent in the Minneapolis suburb of Blaine. She pointed to an apartment recently built half a mile from her house. “It’s beautiful. Way to go. We built our home, so we were the new people on the block 20 years ago.”

“I don’t even think about it,” said Judy Jones about a series of apartment buildings half a block from her home in the Minneapolis suburb of Bloomington. She sounded surprised that she was supposed to be troubled by them. Even for the traffic they cause? Or the strain they put on local schools?

“Oh, no,” she said.

Ms. Jones, 72, grew up in Bloomington, when the local junior high and high school had no African-American students she could recall. “And now I go to my grandchildren’s school, and there is such diversity,” she said. “It’s just amazing.”