Minnie the cow has behaved like a “playful dog” at the East Setauket farm where she’s shown off to birthday children, students and other paying guests — now her owners say it’s time for her to die to feed their family.

A fight over the bovine’s fate erupted this week between Benner’s Farm — also an event and education venue — and animal lovers who want to buy the 2-year-old cow so the “farm mascot” can live out her life at a sanctuary. There has been name-calling, protests slated for this weekend outside the farm, and threats of a boycott.

There is also a Save Minnie from Slaughter Facebook page — 350 friends racked up in less than 24 hours.

“She’s this big, beautiful lush,” said Kimberly Sherriton, 47, of Commack, a cat and dog rescuer who started the campaign after learning of Minnie’s fate Saturday during a birthday party at the farm for her son’s friend. “People wouldn’t be bringing their kids for birthday parties there, getting introduced to Minnie the cow, knowing they’re going to be eating the animal the next week. That’s hypocritical.”

Minnie’s owners, Bob Benner, 73, and his wife, Jean, have raised chickens, pigs, goats and sheep at the farm, which dates to 1751, since shortly after purchasing it in 1977. Back then, they both taught in Northport schools and decided one way to save money would be living “off the dirt” — raising the animals to feed themselves and their growing family of four children.

“If I sold her this cow,” Bob Benner said, referring to Sherriton, “I would have set a precedent that I don’t really want to set ... I would have broken that barrier of raising food for my family.”

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The farm’s website includes photos of children hugging farm animals and boasts of “Old Fashioned Family Fun” for visitors who can pick organically grown strawberries. The website also explains that the Benners raise “a variety of farm animals for self-sufficient living.”

While detractors say the Benners can go to upscale markets for grass-fed, humanely raised meat, the farmers said no amount of money can buy quality assurance.

“Our animals have no steroids, antibodies or other additives added to store-bought food,” Bob Benner said. “We do not condone the meat industry’s practices of crowded feed lots, unsanitary conditions, packed transport, inhumane slaughter ... We are lucky enough to have the space and inclination to raise our animals so we know what they eat and are comfortable with their living conditions.”

Bob Benner said he doesn’t hide the fate of his animals from children who visit.

“I’m not saying ‘See that cow over there? That’s going to be a hamburger,’ ” he said. “But if a parent asks, I might look at them and roll my eyes and say ‘Well, it’s a farm and we produce food.’ That’s usually as far as we go.”

Some who’ve never set eyes on Minnie have joined the fight to save her, like Jodie Flynn of East Yaphank, a dental hygienist who set up Minnie’s Facebook page.

Flynn criticized Benner farm ads that say people can “pet and cuddle” animals there, leading her and others to believe the farm is a “petting zoo” where creatures like Minnie would die of old age.

“We’re not asking him to give up his farm and give up all his animals,” said Flynn, 39. “Somebody found something special in this cow. Children love this cow. Why will he not save it? I can’t believe someone would be this heartless ... You choose to eat meat? That’s fine. You introduced this cow into the community. Then how could you say ‘Next week I want to kill it so I can eat it?’ ”

In cattle farms across the country, cows that reach Minnie’s age end up in the grocery store meat department.

Minnie is the only cow now at the farm. The Benners bought Minnie for $100 at a farmers’ convention in Ohio shortly after her birth and drove the calf back to Long Island in their minivan — hence the name. She was born an infertile twin, what’s known as a “freemartin.” In the mother’s womb, the fluids of the male and female fetuses mix, and the female twin, who gets some male characteristics, ends up with smaller ovaries.

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So far, one woman on Facebook said the fight has given her the impetus to finally stop eating meat. Others said they’d wear cow costumes at the protests. Several suggested contacting groups and schools to organize boycotts of the farm.

Sherriton said a Manhattan animal lover has agreed to chip in $3,000 to buy Minnie and officials at a New Jersey animal sanctuary said they would take her.

The Benners said that if they give in, someone later may fall in love with one of their pigs, a duck or a chicken.

Six years ago, a girl did just that with Minnie’s predecessor, a black and white steer named Patty O’Cloud. The girl’s mother offered to buy Patty O’Cloud and send him to a sanctuary, but the Benners resisted. A Suffolk farm owned by the county later slaughtered the steer for the family.

That farm has since closed. Bob Benner said the only reason Minnie is still alive is because he has yet to find a slaughterhouse.

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Although ending his animals’ lives is still hard, he remains “stubborn enough” to resist calls to let Minnie live, he said.

“Will I feel for this animal?” the farmer said. “Yes, I feel for this animal. But its fate is what we’ve decided it’s going to be.”