You know, I can understand this. Cows cannot come into my house either; I don't care if it IS the movie star from the Milk (Gracie! <sobbing cow>) commercial. She'll sit on the front lawn or be on her way.... About the squirrels: living in the central valley, I haven't had that particular critter problem although we do have a lot of farm animals, as you can imagine. However, I live by one iron-clad rule: I never allow farm animals in my house. Call me inflexible, but I simply refuse to budge on this issue. If I don't eat beef, I don't think I should feel obligated to entertain cows inside my house.
The squirrels who run the fence line here have some kind of issue with Zoey that quite often ends up in a staring match; of course, the squirrel is high up a pole staring down when it happens. I will not begrudge Zoey a little squirrel meat when it happens. And it will.