Islam forbids Muslims to wastefully spend their money, even in permissible and lawful things. Almighty Allah describes the characteristics of true believers and says: “And those who, when they spend, are neither prodigal nor grudging; and there is ever a firm station between the two.” (Al-Furqan: 67)
Basically, it is permissible to buy and keep stuffed animals or birds, because there is no religious evidence that prohibits this. However, if these leads to the wasteful spending of money, it is considered prohibited due to this reason. Islam prohibits the wasteful spending of money and extravagance. We have seen many people spending thousands of dollars to buy a stuffed bird or animal. This is surely extravagance, which must be avoided.
The prominent Muslim scholar Dr. Ash-Sharif Hamza Al-Fi`r, a prominent Saudi Muslim scholar states: “Stuffed birds are neither impure nor decayed. Thus, it is permissible to collect them for the purpose of using it for learning or beautification.”
The prominent Muslim scholar Dr. `Abdullah Al-Faqih, supervisor of Fatwa Centre at www.islamweb.net, Qatar, adds: “Stuffing is a process in which the animal’s skin is treated chemically or in a certain way so as to keep it safe from decay. This is done for the purpose of using the animal or bird either in the pursuit of knowledge or in beautifying the house. As far as Islam is concerned, this is not haram, for there is no evidence to say so. Drawing a similarity between such things and statues is not correct because they are the exact creation of Allah, not an imitation of it. However, if this leads to the wasteful spending of money or extravagance, it becomes impermissible for this reason. The Prophet (peace and blessings be upon him) says: “Allah dislikes for you gossiping, asking too many questions and wasting money.”“