Is money earned from classifying videos that contain images of immodestly dressed women and haram songs permissible, knowing that the sound of the songs is muted during classification, and that these videos are used to train artificial intelligence and may not be published?

The ruling on work relates to the nature of the work itself and its impact. If the questioner can avoid forbidden acts such as muting the sound and lowering her gaze, then there is no sin upon her. As for the impact of the work, which is providing artificial intelligence with the video type to facilitate access for researchers, it aids both those seeking good and those seeking evil. Anything that falls into this category is not forbidden unless the forbidden use predominates, in which case the ruling shifts to prohibition. An example of the second scenario is the sale of singing slave girls (qaynat); because their predominant use was in forbidden acts, their ruling concerning the prohibition of their sale was made the same as something that has no lawful benefit, treating the majority as the whole. If the questioner has no knowledge, she should act based on predominant conjecture, because Sharia rulings are built upon predominant conjectures. If there is neither knowledge nor predominant conjecture, then she should act according to the original ruling, which is the absence of prohibition.