Mushrooms are not from the animal kingdom, Basically, they are fungi. They can be considered vegetarian as it is not an animal or animal-derived product. They are not plants also.
As per the biological classification, there are five divisions :
Plants, Animals, Fungi (mushrooms, yeasts, moulds etc.), bacteria, and archaea.
From the above, vegetarians never eat Animals.
Veggies will not animals or products derived from animals.
Many people eat vegetarian and vegan food for their health and also avoid damaging the earth and animals, Mushrooms are not from animals, Eating them will not harm our body and that will not harm the earth or animals. Hence I feel there is no problem for a vegetarian to eat Mushrooms.
Basically mushroom are rich in proteins and by consuming these we will get good protein food. The other foods which are having good protein content are beans,
I am a vegetarian and I eat mushrooms as I consider mushrooms as vegetarian based on the above point.
But all mushrooms are tables. There are some mushrooms that grow in open under normal conditions of a rainy season may be poisonous and those are not for eating.
Mushroom growing is an Industry and they will grow mushrooms under controlled conditions. In addition to proteins, they will have Vitamins and complex carbohydrates. They are all good for health. These days the product is gaining popularity as a good food product.