Mushrooms are generally considered as vegan-friendly because they are fungi and do not belong to the kingdom Animalia. Being fungi, mushrooms do not have a central nervous system and hence do not feel any pain when we pluck them and chop them into pieces.
 
There has been some debate over whether oyster mushroom is vegan or not because they attract nitrogen-rich prey like small roundworms to derive nutrition.  Fungi are more similar to plants, and because both are not animals, many think it right to consider mushroom as vegan-friendly.
 
If a vegan chooses to avoid mushroom from their diet by regarding it as non-vegan, then they would have to give up baked goods like bread that are made using yeast, a fungus. If you think that mushrooms are non-vegan because they are grown using animal products, like animal manure, it would become hard for you to treat even vegetables as vegan. Many fertilizers and compost used to grow vegetables are made from animal waste or bones.