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Farmers want Shane Jones to keep out of their business and leave them to deal with Fonterra.
The Regional Development Minister is standing by his statements about the dairy giant, which included saying it was out of touch with the farming community.
Mr Jones said the co-operative's chair John Wilson should "catch the next cab out of town" and that it needed to be restructured.
His comments have been supported by New Zealand First leader Winston Peters.
But Waikato dairy farmer Lloyd Downing has labelled them as "completely irresponsible", an "absolute disgrace" and he wants Mr Jones sacked.
"There's 10,000 farmers that own Fonterra. We will decide how Fonterra is set up and if there was going to be any changes."
Mr Downing agreed that there were issues with Fonterra, such as the inability to sell his shares in the company and continue to sell his milk to them, but it was farmers' business.
Lichfield dairy farmer and Fonterra supplier Craig Litten said it was not a politician's place to get involved in the operations of the co-operative or any other private company.
He said while there might be problems with Fonterra, as shareholders, farmers could raise those with the board and have their say.
"I think in general Fonterra does a lot of great things, but I guess they can't get absolutely everything right and yeah I'm extremely disappointed with some of the investment decisions."
In March, Fonterra announced a first-half $348m loss, and its chief executive Theo Spierings stepped down on the same day.
The main reason for the slump was a write-down of $405m in the value of its stake in Chinese food company, Beingmate.
Fonterra bought a nearly 19 percent of the company in 2015 for $750m, but its shareprice slumped amid poor earnings and questions over its management and strategy.
Fonterra also had to account for $183m damages to French dairy company Danone for losses caused by the botulism scare of 2013.
Rakaia dairy farmer Scott Carnochan agrees Fonterra has had its troubles, but he does not like Shane Jones's approach, calling it bullying.
"They're in a bit of a hard spot just now, they are going through some changes, I think it's a big call for him to say that he [John Wilson] needs to leave straight away.
"It's a hard one, I can see what he's talking about, I don't know if he needed to come out and publicly say it though."
The government is reviewing the 17-year-old law which governs Fonterra, the Dairy Industry Restructuring Act.
Ashburton farmer Rhys Roberts used to supply Fonterra, but does not anymore.
He said it looked like Fonterra had fallen out of political favour, and he echoed Mr Jones's comments that the co-operative's leadership had not accepted that there was a new government.
"There needs to be a review into how the board and management is handling, a, the exit of their CEO, and b, how they're dealing with the government."
Mr Roberts said he thought Fonterra might be trying to influence the government on the review.
"Working with them rather than working against them is the best way forward and potentially acknowledging that we have had a change of government."