As others have mentioned, it makes sense if it's for political reasons; there's a lot of animal cruelty and a certain degree of unsustainability (a pound of pork costs ~10x the energy and arable land to produce as a pound of corn, which wouldn't be a problem with a better distribution system but is a concern given the way the world works now) involved in the modern livestock industry, which one could reasonably extrapolate Diana washing her hands of and refusing to participate in. (Plus, growth hormones and that kind of thing might bug her.) It makes sense for her to not eat meat anywhere where she can't verify the source, and then go home and rock out on venison or have homegrown chicken at the Kent farm or whatever.
The problem is, Rucka doesn't remotely present it that way - the only explanation he ever gives is "if you could talk to animals, wouldn't you be a vegetarian?" which is so much bullshit it's ridiculous. One of the other aides follows it up with "that's not the only reason..." but if there's more, we never hear about it, and they all seem pretty sure that that's a major contributing factor. Major misfire on his part.