How can I make Agricola vegetarian friendly?
The game already supports this with improvements like Pottery, which converts clay to food. Clearly, the imagined implication isn't that suddenly your family has a fulfilling case of pica — it's that the clay is used to make some good which can be exchanged for food (and that's abstracted away). 

Imagine something similar for animals in the game, and there you go. (Of course, you'll still have to part with the animals — let's happily imagine that they are unharmed in that parting.)

Of course, if your friends follow the strain of veganism which holds that all animal agriculture is bad, this won't do, and you'll have to reskin the whole game significantly.