The council has introduced 'meat-free Mondays' - allegedly without consulting parents first - this term, despite vegetarian options already being available five days a week.
Elizabeth Sellers, whose family have an arable farm at Kilham, near Driffield, believes the issue over meals for her seven-year-old daughter is about 'choice' and supporting farming and food production in the local area.
"The point is not meat-driven, but the lack of choice - every day there is an option for vegetarians, but the meat-free day has no choice for a meat eater.
"We are a rural area, we are thankful for our hard-working farmers and the associated agricultural and food sectors and the high quality food on offer. As a parent I would like my child to have a choice and be able to make that choice. For other parents, it is the way it is being sold as a positive thing to be meat-free.
"Let’s get behind our farmers and food industry and give children a choice. This is dietary dictatorship and I’m sure many people will be saddened to see this is happening in their local primary school."
Although schools have the choice to 'opt out' of the scheme and her daughter's school now has, Elizabeth believes other headteachers will not be aware that they can choose not to take part.
"It's inappropriate branding in a school environment, and there's no rational or motivational reason given behind the message, whatever the message is.
"The issue is the lack of support for our agricultural industry and food sector which contributes to the economy through jobs and income for the area.
"I suggest if schools feel strongly the school community should ‘opt in’ to this scheme rather than have to opt out.
"I live on a farm and am part of an arable farming family, but farmer or not, this is about freedom of choice and poor wording. My daughter loves school and loves school dinners too.
"Councillor Jane Evison has worked very hard to get to the bottom of this, along with our headteacher and others locally who have been excellent in supporting the school so that dinners remain without meat-free Monday. Highlighting choice is important."
Bridlington butcher Richard Smith, who runs Smiths Butchers, has also voiced his opposition to the introduction of meat-free Mondays in local schools.
Posting on his business's Facebook page, he said: "It has been brought to our attention that East Riding Council have introduced meat-free Mondays for school meals. Now this isn't us trying to have a dig at vegans or vegetarians as we respect their views and opinions. Our point is that there is a vegetarian option everyday but NO meat on a Monday. Surely children or parents should have this choice and not be forced into vegetarian meals?
"We respect everyone's views and also have vegetarian customers."
East Riding Council are now expected to launch a further consultation about school menus.
Commercial strategic manager David Johnston said: "As children’s tastes have changed, we are now being asked to produce recipes and menus which are suitable for vegetarian and vegan diets on a more regular basis.
"The options we are offering on Mondays are dishes which have proved popular previously and we have worked to ensure that the menus conform to school food standards.
"Individual schools have the option to change the menu, with direction from the head teacher and governing body, as long as the menu adheres to the food standards set by the government.
"The Catering Services Team will consider the feedback to the new menu and will consult with our schools, looking at alternative options, if schools feel it is appropriate."
Meat served in schools in the East Riding is sourced from accredited suppliers in the Yorkshire and Humber region.