The groups held a candlelight vigil Friday evening at Jordan Park for the slain woman, Norma Hernandez Espinoza, who was killed June 10 outside a West Valley City apartment. About 70 people attended.
"We must combat the voices of those who hate," said Gena Edvalson, the gender justice coordinator at Utah Progressive Network, in a news release, "and we must stand together as friends and neighbors to show that we, as a community of love and understanding, are a greater force than hate and violence."
The alleged killer, Trey Holloway Brown, has been charged with first-degree felony murder.
Espinoza - who was having a romantic relationship with Brown's wife - had joined in a heated argument Brown and his wife were having about their three children when Brown grabbed a kitchen knife and chased the victim into the parking lot.
Outside, Brown stabbed Espinoza three times, then jumped up and down on her chest and kicked her in the head, according to witnesses.
Court documents describing the charges make no mention of the victim's sexual orientation.
"We charged [Brown] with murder, which was the highest crime that he allegedly committed, and we found no evidence a hate crime under Utah law was involved," said Deputy Salt Lake County District Attorney Robert Stott.
Said Edvalson: "We must say no to violence against women and violence against lesbians."
David Nelson, founder and owner of Stonewall Shooting Sports of Utah, issued a news release calling for women to arm themselves.
SSSU is a group of sexual-minority firearms advocates and owners who recommend gay and lesbians carry guns for protection. The so-called "Pink Pistols" idea was coined by writer Jonathan Rauch in 2000.
"Women with firearms are up to 2.5 times less likely to be injured," Nelson said. "Every year, people in the United States use a firearm to defend themselves against criminals more than 2.5 million times - several times more often than criminals use firearms to commit crime.
"Clearly, the legal, responsible and safe use of firearms saves lives and probably would have saved the life of Norma Hernandez Espinoza."

