Is it permissible to take money from YouTube in exchange for publishing religious lessons and permissible content, knowing that the ads appearing on the videos contain prohibited things?

If she takes a wage for publishing forbidden advertisements, then this is not permissible, regardless of the source of the wage. Working for a Jew or a Christian is permissible, provided that the work itself is permissible. As for forbidden work, it is not permissible to take a wage for it, whether from a Muslim or a non-Muslim, and whether the wage is paid from lawful or unlawful money. If you have the choice of the advertisements published and control them so that you only publish what is permissible, then there is no harm in profiting from them. However, if you do not have the choice of the advertisements and they are forbidden, then the wage for them is not permissible.