The food system is not easily grouped into "climate-conscious" and "bad"; a vegan diet is better than a western one in every study I've seen, but we could do much, much better.
I highly recommend this study as a starting point, though you need to convert the unit they use, kg CO2e / kg, to the unit we eat in, kcal: https://www.sciencedirect.com/science/article/pii/S095965261...
And, shameless self-promotion: I maintain a food blog that attempts to build an evidence-based low carbon collection of recipes at https://www.carboncook.com