Does a poisonous caterpillar turn into a poisonous butterfly?

There are many, many different species of butterfly, so in order to provide some kind of answer let's consider only the Monarch butterfly.

Monarchs feed on milkweed, which contains a compound that is poisonous to most birds and mammals. The compound builds up in the caterpillar's body, making the caterpillar itself also poisonous. When metamorphosis occurs, the toxins remain, so the butterfly is also poisonous.

Over time, unless the butterfly continues to consume the toxins, they eventually become less poisonous. Also, toxin levels vary from species to species and variety to variety of milkweed; even different parts of the same individual plant may have different levels. So a given butterfly may be poisonous but another one of the same species may not be, depending on exactly what their diet was.