Every time someone ripped down the rainbow Pride flag from the Mag.Pi clothing store in the San Bernardino mountains in California, the store’s owner, Laura Ann Carleton, responded by putting up a bigger one.

Ms. Carleton, 66, did not waver in her support of L.G.B.T.Q. people.

Around 5 p.m. on Friday, she was fatally shot by a man who made disparaging remarks about the shop’s Pride flag, the authorities said.

The man, whose identity has not been released, fled the scene on foot. Deputies found him with a handgun, and he was killed in an encounter with law enforcement, the San Bernardino County Sheriff’s Department said in a statement.

The department said that “detectives learned the suspect made several disparaging remarks about a rainbow flag that stood outside the store before shooting Carleton.”

It was unclear whether the shooting was being investigated as a hate crime, and additional details of what preceded the attack were not available on Sunday. Sheriff’s Department officials were not immediately available to comment.

The shooting — in Cedar Glen, near Lake Arrowhead — came about a month after the Anti-Defamation League and the L.G.B.T.Q. advocacy group GLAAD released a report indicating a recent rise in anti-L.G.B.T.Q. harassment, vandalism or assault in the United States.

Ms. Carleton’s daughter Ari Carleton, 28, said that her mother was “fearless” and put the needs of others ahead of her own. Ms. Carleton had been a pillar in the community, she added.

When a rare blizzard struck the area this year, Ms. Carleton and her husband, Bort Carleton, converted her shop into a relief center.

“She opened up a free shop where she and my dad just gave out supplies to those in need who had been impacted by the storms,” Ari Carleton said in a phone interview on Sunday, adding, “That really sums up who she was as a person.”

Ms. Carleton preached “love, acceptance and equality,” her daughter said, and those values were reflected in her store, Mag.Pi, where she carried a collection of personally curated, high-quality and ethically sourced clothes, and sometimes her own designs.

Paul Feig, the film director, was a friend of Ms. Carleton’s. He would have dinner with Ms. Carleton and friends on his visits to Lake Arrowhead.

“She was just a force of nature,” Mr. Feig said, adding, “She just really cared about people.”

The Pride flag hanging outside Mag.Pi was removed numerous times by different people since the store opened two years ago, Ari Carleton said.

The store is listed as a “business ally” by Lake Arrowhead LGBTQ+, a community group.

“Lauri did not identify as LGBTQ+, but spent her time helping & advocating for everyone in the community,” the group said on Facebook. “She will be truly missed.”

The organization is planning a vigil for Ms. Carleton once the threat of Tropical Storm Hilary clears.

She is survived by her husband and nine children.

“I just want the world to remember her for who she was,” Ari Carleton said. “And that she passed away in a place that she cherished, doing what she loved and defending something that was so important to her.”

At Ms. Carleton’s Lake Arrowhead home after the shooting, her family opened a package that had been left at the doorstep.

The flag at the store had begun to fade, Ari Carleton said. Her mother had ordered a new one.