A transition to healthy diets such as the EAT-Lancet Planetary Health Diet could considerably reduce greenhouse gas (GHG) emissions. However, the specific contributions of dietary shifts for the feasibility of 1.5°C pathways remain unclear. Here, we use the open-source integrated assessment modeling (IAM) framework REMIND-MAgPIE to compare 1.5°C pathways with and without dietary shifts. We find that a flexitarian diet increases the feasibility of the Paris Agreement climate goals in different ways: The reduction of GHG emissions related to dietary shifts, especially methane from ruminant enteric fermentation, increases the 1.5°C compatible carbon budget. Therefore, dietary shifts allow to achieve the same climate outcome with less carbon dioxide removal (CDR) and less stringent CO2 emission reductions in the energy system, which reduces pressure on GHG prices, energy prices, and food expenditures.