"A full weight of a cowboy knee block restrain used on a horse's face after it has fallen," the caption stated. "We are against this treatment on both animal and human."
A number of posts published since use photos and videos from rodeos, including of calf roping, alongside a photo of Prime Minister Jacinda Ardern with captions including, "PRIME MINISTER - I CAN'T BREATHE" and "ALL LIVES MATTER".
"I CAN'T BREATHE," one post of a video of calf roping was titled. "The Ardern government reneged on its promise to stop calf roping. This poor boy was strangled twice."
Some people called on the group to remove the posts.
"Check your privilege and have some respect," one woman wrote. "Delete this post and educate yourself."
"As much as I support this cause, do you not think co-opting phrases associated with another important cause that a lot of people are upset about is a little tone deaf?" a supporter commented.
"Awful stuff, the poor calves," another person commented. "However, I really wish you wouldn't use Eric Garner and George Floyd's dying words…"
Others pointed out one of the posts initially hadn't used a photo of Ardern but rather comedian Melanie Bracewell impersonating the Prime Minister.
In a response to one of the negative comments, the Anti-Rodeo Coalition said: "We feel nothing but contempt, sadness and outrage at Eric Garner and George Floyd's deaths, as does any reasonable person.
"If anything good is to come from these evils then we have to take it to the highest level in such a way that will get their attention and get the wheels in motion to engage change. And if these poor men's words make for a better world then those words would not have been fruitless."
The group told the Herald that it was appalled and saddened by Floyd's death, and was against "racism, police brutality and animal brutality".
"But the paradox for the Jacinda Ardern Government is that they have allowed baby animals to be systematically choked and killed for entertainment against SPCA , NAWAC [the National Animal Welfare Advisory Committee] and every animal advocacy in New Zealand and yet still perpetuate the 'be kind' mantra.
"Especially after the Ardern Government made a specific promise to ban calf roping and several aversive aspects of rodeo and renegade.
"In no way whatsoever do we mean disrespect to George Floyd. Ours is a stand against brutality, racism and violence."