Is it permissible to use a video clip containing the voices of other people who have not given permission for its publication? And what is the ruling if the clip is uploaded and then one of them objects to their appearance?

Recorded speech is ordinary, and there is nothing to prevent its dissemination, as long as it is free from any Sharia-prohibited elements. However, it is not advisable to excessively disseminate or become preoccupied with such audio clips.