The Vegetarian Star gives us a little background about Brennan being a vegetarian as opposed to being vegan like ED herself.
“I can’t remember if it was my idea or not. I didn’t want her to become vegan–and she’s vegetarian for health reasons, not because of animal rights. It’s important to keep a separation between actor and character. I do always ask for episodes touching on animal rights in the same way. And I ask that there’s a character to present the case for animals in every episode.”You can find the whole article here.