A report to the full council had recommended that the 10p charge for a 189ml serving of milk in the area's council-run primary schools should be removed, at a potential financial cost of £21,000 to the authority.
When the matter was discussed, rival councillors clashed over the Scottish Government's record on education before the recommendation was agreed.
The virtual meeting took place on Thursday, June 24 – the same day First Minister Nicola Sturgeon fielded questions on the Scottish Government's education record in the Scottish Parliament.
A council officer also revealed plans to involve pupils in taster sessions to help further develop menus for school meals.
New regulations set by the Scottish Government have limited the amount of sugar, red meat and processed red meat that can be used.
Councillor Jim Anderson, Dunoon, said: 'I welcome this paper – it is the way forward. I am also wondering how free school meals will affect the uptake.
'If the new menus discourage kids from having meals, how will that apply? But that is for another day.'
Ross McLaughlin, the council's head of commercial services, said: 'The new menus came into effect in April and these are part of new national requirements to reduce sugar and processed red meat.
'This is the first round and we will take feedback into consideration. When Covid restrictions allow, we will also have kids in for tasting sessions and we hope this will keep uptake as high as possible.'
He also pledged that once the 2021/22 term starts, figures for uptake to date will be collated and shared.
Councillor George Freeman, Lomond North, asked: 'Given that the Scottish Government seems to be becoming more green these days, is it not possible that they might be looking for local authorities to remove red meat, and possibly all meat, from menus?'
Mr McLaughlin said: 'I cannot predict what the Scottish Government will do next, but certainly they have reduced the quantity on a weekly basis that schools can provide. We try to procure all of our goods as locally as possible.'
Councillor Gordon Blair, Cowal, said: 'To reassure Councillor Freeman, the Scottish Government will do its best to ensure kids are eating properly.
'I welcome this move to allow milk to be part of a reasonable diet. It is all part of a strategy and it is all on the Scottish Government website, bringing kids out of poverty and giving them diets allowing them longer, more fulfilling lives.'
Councillor Yvonne McNeilly, Cowal, the authority's policy lead on education, responded: 'What planet is Councillor Blair living on, given the excoriating report the SNP have regarding the exam situation?'
The recommendation to remove the 10p milk charge was unanimously agreed.
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