personally I've never had a problem with animals eating toxic plants. When I started with sheep I'd've struggled to identify half the poisonous plants in my fields, let alone removed them all.
I found a yew tree in my field only after the sheep had eaten the green ivy that had covered it. In my current fields I have leylandi, laburnum, bracken, foxglove, deadly nightshade & ragwort (though that's only a worry in hay); there's probably more that I haven't yet identified - certainly there're things they don't eat. Before I moved here my farmer neighbour grazed his cattle into the same fields without issue.
I also let the sheep, lambs, pony & chickens into the garden to eat the grass & weeds from around the rhubarb - which they do without eating it - although the pony tends to trample the rhubarb a bit.
I did once have a ewe get ill after (possibly) eating green acorns from a fallen tree, but that's not certain - but she'd always had a bit of a taste for acorns.
Having said all that there have undeniably been cases of animals eating yew, so I suppose there's a small risk if you happen to have an animal whos' instinct/sense of taste are a bit off.