Is it permissible to work for a variety website that includes religious and worldly sections, as well as songs, if the work is limited to writing articles in permissible fields?

So long as your work is specialized in writing beneficial articles that do not contravene Sharia, then your work is permissible, and your earnings from it are lawful. The fact that the website publishes other forbidden things does not make your permissible work unlawful for you.