Is it permissible to download videos from YouTube using specialized programs for that purpose, especially if the videos are religious and their owners do not object to free distribution, while YouTube prohibits downloading?

It is not permissible to download clips from websites that prohibit it, except with their permission. The benefit from them is restricted to viewing and listening. Although some scholars permit copying for personal use, not commercial, as Ibn Uthaymin فتوى (religious edict) stated, it is hoped that there is no harm in that, especially when there is a need for beneficial programs and books that are difficult to obtain.