Is shed cat’s fur najis (impure)? And is a prayer invalid if there is a cat’s fur on a person’s body when he’s praying?
Basically, a cat’s shed fur is categorized as najis according to madhhab Syafie. However, it is forgiven if it is in a small quantity. It is also forgiven for those who work as a veterinarian, zookeeper and other occupations where it is unavoidable for him to interact with cats. This is stated by Syeikh Ibrahim al-Bajuri as the following:
وخرج بالمأكول غيره كالحمار والهرة فشعره نجس لكن يعفى عن قليله بل وعن كثيره فى حق من ابتلى به كالقصاصين
“The exemption for the ruling of animals that are permissible to be eaten (its fur is permissible) other than donkeys and cats. Hence, its fur is najis, but it is forgiven if it is a little. Furthermore, (it is forgiven) in a large quantity for individuals who experienced difficulties such as if he is a shearer.” 
Nonetheless, to avoid khilaf, it is best to ensure one’s clothing is clean and free from any cat’s fur before praying. However, if a cat came and rubs itself when we are praying and left some of its furs, then it is forgiven according to the opinion of some Syafi’iyyah scholars for it is unavoidable. Wallahua’lam.
 Hasyiyah al-Baijuri ala Ibn Qasim al-Ghazi, 2/290