Joining a chorus of fury directed at the council was acclaimed British comedian and television star Ricky Gervais, who last night tweeted a link to the story with the remark: "Stupid c****."
The story was also shared by fellow funnyman Tim Dillon, who asked: "What the f*** is going on over there?"
Bourke Shire Council has gone to ground since the dogs' deaths were exposed and a NSW Government investigation has now been launched.
Lisa Ryan, the regional campaign manager for Animal Liberation, told the Sydney Morning Herald she was sickened by the decision.
"We are deeply distressed and completely appalled by this callous dog shooting and we totally reject council's unacceptable justifications that this killing was apparently undertaken as part of a Covid Safe plan," Ryan said.
The shelter in Cobar reportedly had Covid-19 safety measures in place. Its volunteers are said to be deeply distressed by the shooting of the dogs.
In a statement, the Office of Local Government – the authority that oversees local councils – confirmed an investigation was under way.
"The OLG has been informed the council decided to take this course of action to protect its employees and community, including vulnerable Aboriginal populations, from the risk of Covid-19 transmission," the statement read.
Despite harsh restrictions across the state, the NSW Government has told animal shelters they can continue to operate with Covid-safe plans in place.
Cobar hasn't had any cases of coronavirus during this current outbreak.