“In 2019, this type of behavior should not be accepted because of certain views,” she wrote. “If you don’t want to sit next to certain people in a public restaurant then you should probably eat dinner in the comfort of your own home.”

She said the families left and went to a nearby Hooters restaurant. Ms. Vahl thanked that restaurant in her Facebook post “for serving our group and the patrons of Hooters for not being close-minded people that would ruin the night of others.”

Buffalo Wild Wings did not identify the managers who were fired, or describe the episode.

On Tuesday, several members of the group were joined by a lawyer at a news conference at a church in Naperville, where they recounted the incident and answered questions.

“This is a tough time for us,” said Justin Vahl .

“I was appalled. I was astonished,” Mr. Vahl said, referring to when the host asked him about his race. “What does that matter?”

Another member of the group, Marcus Riley, who is a children’s basketball coach, said the experience had been “confusing” for the children, who he said were worried they had done something wrong.

“How do you translate this message?” he asked.

Cannon Lambert, the lawyer at the news conference, said no lawsuit had been filed.

“This is the perfect opportunity for Buffalo Wild Wings to be a good corporate citizen,” he said.

Mr. Lambert said he was “maintaining a dialogue” with the company to make the space “safe and comfortable” at outlets nationwide. He read a list of “practical applications” that the company could do, including employee screening to ensure applicants are sensitive to diversity and inclusion; a handbook that explicitly states a zero-tolerance policy; an employee hotline to report racist activity; and including Mr. Vahl and Mr. Riley in sensitivity training for employees.