Others say substitutes such as soybeans or kidney beans, suggested by an Iskcon official, are not widely eaten in the state and may not be readily accepted by students.
Some politicians and activists have proposed a middle path: let students choose between eggs and a vegetarian alternative.
Eggs have long been considered one of the cheapest and most efficient sources of high-quality protein. They usually cost around eight rupees ($0.08; £0.06) each and have been part of Bengal’s food culture for generations.
Defending the decision, Chief Minister Suvendu Adhikari said the project was aimed at providing students with “good and pure food”.
“You don’t have to say Hare Krishna (the movement’s devotional chant). No one will force you,” he said, rejecting criticism that the move was driven by the BJP’s Hindu nationalist ideology.
Iskcon says the criticism is misplaced. Through the Akshaya Patra Foundation, which it founded, it provides school meals to about one million students across 16 states, including Karnataka, Andhra Pradesh, Gujarat and parts of Delhi.
Radharaman Das, Iskcon’s Kolkata vice-president until last week, told local media that the organisation takes special care to ensure its meals are nutritious and hygienic.
He said the vegetarian menu would provide enough protein and vitamins to match the nutritional value of eggs.
Das has since been removed from his organisational posts, although Iskcon has not publicly explained the decision.
The BBC has contacted Iskcon for comment.
The row has also renewed focus on India’s school meal scheme.
Launched nationwide in 1995, and rooted in a school feeding programme begun in Madras (now Chennai) in 1925, it has grown into one of the world’s largest, serving more than 110 million children.
The federal government sets calorie and protein targets, but states decide how to meet them. As a result, there is no single national menu, and meals vary across the country.
In Bihar, children are typically served rice with pulses or chickpeas, plus an egg once a week. In Tamil Nadu, school lunches often include rice, sambar (lentil-vegetable stew), vegetables and eggs.
Other states serve only vegetarian meals. In Gujarat, Uttar Pradesh and Delhi, menus usually feature rice- or wheat-based dishes with pulses and vegetables, sometimes accompanied by milk, paneer (cottage cheese) or fruit.
How meals are prepared also varies.
In many government schools, they are cooked on site by dedicated staff. Elsewhere, state governments contract non-profit organisations to prepare and distribute meals that meet prescribed nutritional standards and state menus.
For nearly a decade, students in Kolkata’s government schools have been served an egg on some days of the week, alongside rice, pulses and vegetables. Now, that could change.