Is it permissible to describe a non-Muslim as a "disbeliever" (kafir), even if they acknowledge another religion, and is this exclusively for scholars to do?

Whoever believes in a religion other than Islam or commits major disbelief (kufr akbar) is a disbeliever (kafir). However, it is not wise to address a disbeliever with "O kafir!" because it causes alienation and obstinacy. Sheikh Ibn 'Uthaymeen advised saying, "If you do not repent to Allah, then you are a disbeliever," instead of direct address. As for informing about a person's disbelief when there is a need, there is no harm in it.

As for a Muslim who falls into a matter that might involve disbelief or is suspicious, they are not declared a disbeliever except after the establishment of proof (iqamat al-hujjah) against them. As Sheikh al-Islam Ibn Taymiyyah mentioned, one whose Islam is established with certainty does not lose it except after the establishment of proof and the removal of doubt. Ibn 'Uthaymeen pointed out that a statement might be disbelief (kufr), but its speaker is not judged to be a disbeliever if they are excused or ignorant until their situation becomes clear. Declaring someone a disbeliever in such cases is referred back to the scholars.