Our World in Data has published this piece, which breaks down the extent to which the differences in carbon footprints of food categories can be attributed to methane, a short-lived greenhouse gas which has attracted controversy over how its climate impact is measured.
The piece bases its data on the 2018 Poore and Nemecek paper Reducing food’s environmental impacts through producers and consumers. The figures used are global averages and do not account for the variation in carbon footprint between different regions or different types of production systems (although Poore and Nemecek do discuss these variations in their paper).
The piece explains that - while methane causes a significant fraction of the climate impacts of many foods - the hierarchy of food carbon footprint holds true regardless of whether methane is counted towards a carbon footprint or not: red meat, chocolate, coffee and prawns have high carbon dioxide footprints as well as total (carbon dioxide plus methane) carbon footprints, while most plant-based crops have relatively low carbon footprints with or without methane, as shown below.
The piece also applies the same treatment to protein-rich foods, as shown below.
Read the full piece The carbon footprint of foods: are differences explained by the impacts of methane? here. See also the Foodsource building block Agricultural methane and its role as a greenhouse gas.