People needing to eat would be the equivalent of people needing energy in this scenario.

People need to eat specifically meat like they need to burn specifically coal and oil.

They don't need to eat beef though, emissions from other meats are much lower.

Lowering dairy and beef consumption would go a long way to reduce that damage.

People need to do and same goes for some of our food. As it relates to cows, there is research showing that the emissions they produce are dependent on their feed, and that methane in particular can be reduced through the use of additives such as seaweed. However, it's not clear that this particular strategy would be effective in the long-term, and we would need to produce a LOT of seaweed in order to have a significant impact.

Changing food production is possibly one of the easiest ways to attack climate change, as far as physical/biological feasibility goes (desires of tastebuds notwithstanding). Nobody trying to tackle food production suggests you should become malnourished for the sake of the climate.