What is the ruling on publishing websites in a directory that includes sections for songs and movies, knowing that the websites intended for publication have no relation to these sections?

If the topic you wish to publish in the aforementioned directory does not contain forbidden matters, then there is no blame upon you. Rather, you will be rewarded, Allah willing. It does not harm you that the directory contains sections for forbidden songs and movies, as long as you do not assist in them or contribute to them. You should advise those in charge of the directory, if you are able, while clarifying the danger of these forbidden things.