They don’t always.
Sometimes they eat a poisonous thing and regret it. Here’s a famous picture of a blue jay that ate a poisonous monarch butterfly, and puked.
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If the poisonous thing is aposematic, they won’t make the same mistake again. Monarchs happen to display their toxicity with bright colors, as do most toxic animals and any animal that tries to look toxic. If you see something really colorful and striking in nature, it’s probably chemically defended. Otherwise, its coloration would make it instant prey.
Sometimes they eat a poisonous thing and have mechanisms to deal with it. Certain plants contain chemicals called psoralens, which cause photosensitization. Eat too many, and you will sunburn more easily. Wild parsley is a good example. Certain insects eat this plant, and then hide in the shade for a few hours until their body has passed the compounds. They avoid the toxin’s effects through an evolved behavior!
Sometimes they eat a poisonous thing and suffer or die. Many stories exist of cows eating parsley and going blind, because their retinas burned out because of the psoralens. Poisons do work in the wild, and not all animals know what to avoid. A tragic example is Australian animals and the poisonous cane toad, introduced to Australia by humans. Few Australian animals can eat it, but many try and the introduction of this toad is exacerbating the demise of much native Australian fauna.