The union representing Santa Clara police officers said some of its members may not work at 49ers games over comments made by quarterback Colin Kaepernick about race and policing.

The Santa Clara Police Officers’ Association called Kaepernick’s criticism of police and his decision to sit during the national anthem in pre-season games “inappropriate workplace behavior,” according to a letter the union sent to the 49ers.

“The board of directors of the Santa Clara Police Officers’ Association has a duty to protect its members and work to make all of their working environments free of harassing behavior,” the union wrote in the letter, which members hand-delivered to 49ers officials, the letter said.

The Santa Clara police department, whose members are represented by the union, is among several law enforcement agencies that staff 49ers home games. Union officials couldn’t be reached Friday, but a spokesman for the police department said he had no comment.

In a community message released Saturday morning, Santa Clara Police Chief Michael Sellers promised that there would be a safe environment at Levi’s Stadium.

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While “many of us in the law enforcement community have been saddened and angered by Kaepernick's words and actions ... the safety of our community is our highest priority,” Sellers said in his email. “I will urge the POA leadership to put the safety of our citizens first. I will work with both sides to find a solution.”

The 49ers will open their season at home against the Los Angeles Rams on Sept. 12.

The threat — which drew immediate condemnation from prominent activists on Twitter and on the union’s Facebook page — is part of the growing reaction from law enforcement agencies and police unions over Kaepernick’s statements, in which he assailed police shootings and racial injustice.

“There’s a lot of things that need to change,” Kaepernick said Sunday. “One specifically? Police brutality. There are people being murdered unjustly and not being held accountable. People are being given paid leave for killing people. That’s not right. That’s not right by anyone’s standards.”

Kaepernick also argued — which police were quick to contradict — that training to become an officer is minimal.

“You can become a cop in six months and don’t have to have the same amount of training as a cosmetologist,” Kaepernick said. “That’s insane. Someone that’s holding a curling iron has more education and more training than people that have a gun and are going out on the street to protect us.”

In a letter to 49ers President Jed York and NFL Commissioner Roger Goodell, San Francisco Police Officers Association President Martin Halloran called the comments “foolish” and said they represented “naivety and total lack of sensitivity towards police officers.” The Alameda County Sheriff’s Office waded into the issue this week, too, inviting Kaepernick to a training session.

The warning from the Santa Clara police union elicited a swift response from activists and community members.

“It's telling that when you say that the police can't just kill people anymore they say they'll stop working,” DeRay Mckesson, a leading voice in the Black Lives Matter movement, wrote on Twitter.

Kimberly Veklerov is a San Francisco Chronicle staff writer. Email: kveklerov@sfchronicle.com Twitter: @kveklerov