What is the ruling on women and children watching TV series that contain unveiled women and music, when the viewer does not intend to watch such things, and is this action permissible based on the fatwa of some preachers allowing viewing without the intention of listening?

Perhaps the Sheikh meant the permissibility of watching documentary or educational films accompanied by musical instruments if their content is beneficial and needed by the viewer, and there is no alternative available; due to necessity and widespread affliction, and based on the distinction between unintentional hearing and intentional listening. As for TV series and the like, which waste time and for which there is no need, the ruling on musical instruments within them remains forbidden as per its original ruling. The prohibition becomes even more تأكد if they contain other Sharia (definition)-prohibited elements, such as deviant ideas and promotion of immorality.