One creature eating a certain type of food doesn’t make it safe for another. Birds and animals evolve different mechanisms over time to break down poisons, usually in the liver and kidneys.
For example, during a time of famine some 5,000 years ago, some humans – mostly in western Europe – developed an enzyme to break down cow’s milk.
We can therefore hypothesise that a similar evolutionary stimulus would have allowed squirrels to eat death-cap mushrooms and nightshade berries.
Likewise, many species of bird have adapted to eat mistletoe and holly, two berries that are poisonous to humans. Interestingly, mistletoe berries produce a sticky substance in the digestive tract that’s difficult for birds to excrete. When it’s time for an individual to defecate, it has to ‘wipe’ its bottom along the branch it’s perched upon to help draw the gluey waste out. This, in turn, helps to disperse mistletoe seeds.