Praise be to Allah.
The coffee mentioned is produced from coffee beans that are extracted from the faeces of the civet cat (luwak). This animal feeds on the coffee beans, and expels the coffee beans with its faeces, which are then washed and cleaned before being sold.
What we understand from what has been published on this topic is that the coffee beans are extracted in solid form from the animal, as they are, and they do not dissolve in its stomach and do not absorb any impurity.
Based on that, if any impurity that has become attached to them is washed off, they become pure (taahir), and it is permissible to use them to make coffee.
It says in ad-Durr al-Mukhtaar: Barley that is found in solid form in faeces or dung may be eaten after washing.
Ibn ‘Aabideen said in his commentary on ad-Durr al-Mukhtaar (1/349): What is meant is: if the barley is found in the dung of camels or sheep, if it is washed and dried three times, it may be eaten.
If it is found in the dung of cattle, it may not be eaten. It says in al-Fath: Because it is not solid.
Moreover, it is narrated in at-Tataarkhaaniyyah from al-Kubra that the correct view is that it depends on whether (the grain) is swollen or not. This applies whether it is found in the dung of camels or cattle. In other words, if it is swollen, it should not be eaten in either case (whether the dung is that of camels or cattle), otherwise it may be eaten. End quote.
Al-Hattaab (may Allah have mercy on him) said in Mawaahib al-Jaleel (1/105): There was narrated from al-Barzali that which may be understood as meaning that with regard to stones, pits and gold, and other things that do not dissolve, if they are swallowed and then expelled from the stomach, nothing becomes impure (najis) except their outer surface. End quote.
But if we assume that these fruits (coffee beans) are affected by the enzymes secreted in the animal’s stomach and thus absorb impurity, and do not remain solid as they were, then it is not permissible to drink the coffee that is made from them.
An-Nawawi (may Allah have mercy on him) said: Our companions (may Allah have mercy on them) said: If an animal eats some grains and they come out of its stomach in sound condition, then if they remain solid, in that if they were to be planted they would grow, then they are pure (taahir).
But their outer surface must be washed to remove impurity, because even though they were food for the animal, they have not changed and become spoiled. It is similar to the case if the animal were to swallow a date stone which was then expelled; the inner part of the date stone remains pure, and its outer surface may be purified by washing it.
But if it is no longer solid, and if it were planted it would not grow, then it is impure.
These details were mentioned thus by al-Qaadi Husayn, al-Mutawalli, al-Baghawi and others.
End quote from al-Majmoo‘ (2/573).
And Allah knows best.