Animal-based foods tend to have a high environmental impact. A reduction of meat in the diet has been proposed as a strategy to reduce the environmental impact associated with food production. It is widely assumed that alternative proteins, such as highly processed plant-based meat alternatives, cultured meat, or insects, could substantially reduce animal protein consumption, and that this may result in a more sustainable food system compared with the current one. However, we question whether consumption of animal protein will decrease substantially as a result of these alternative proteins. Our research shows that psychological constructs such as food disgust and food neophobia are important barriers to the acceptance of alternative protein sources, such as insects or cultured meat. Furthermore, our survey results from four European countries suggest that plant-based meat alternatives are more widely accepted than insects and cultured meat. Furthermore, imitating processed products (e.g. burgers) is more widely accepted than imitating whole cuts (e.g. steaks). It remains to be seen to what degree alternative proteins will be substitutes for meat. We have some serious doubts that technological food solutions will be sufficient to solve the problems associated with meat consumption. A quick change from animal proteins to alternative protein sources should not be expected.