For example, freshwater consumption is important in regions which lacks freshwater. Crop agriculture is however the most common source for water pollution, occurs in all regions, and is not only a major environmental problem but also harms the supply of fresh water even if its not responsible for the primary consumption. Fertilizers and pesticides being the main culprits here. Sadly there is very little food in stores that do not have a direct link to fertilizers and pesticides except for wild fish, shellfish and seaweed.
In quite a few times I have seen studies showing that the lowest carbon emission in any food group would be either shellfish, seaweed, or insects. No fertilizers, pesticides, herbicides, minimal land usage and sustainable. Vegan would exclude two of those, and seaweed is pretty rare in non-asian diets.
In general I try to look for marks of sustainability when buying food. Small producers, non-factory farm operations, local, crops that are in season, and so on. The article here focus on the issue of sex determining the eggs, but my primary priority is the area that the hen has. In EU you can have 16 hens located in a small box the size of 0.2m². That is plain cruelty and so I choose eggs under the mark that require 4m², a requirement for outside area, always access to natural lighting, and given crops grown without chemical fertilizers, pesticides or herbicides.
Is it perfect? No. Not using fertilizers, pesticides, and herbicides is still being debated and researched if they are better for the environment or worse since land usage increases from it, but since I regularly dive in the Baltic sea I am constantly reminded by the harm done already by the revolution of chemical fertilizers produced primarily by natural gas.