Is working as a programmer for an application - such as YouTube - permissible or impermissible, given that it displays everything the user requests, whether it be Qur’an or songs?

It is permissible to work for applications that are used for both lawful and unlawful purposes, unless it is highly probable or known that they will be used for unlawful purposes. However, if the predominant use of the application is for unlawful acts, then working for it is forbidden, because the ruling is based on what is predominant.