Thanks for reaching out. Songs that appear grayed out in iTunes need to be downloaded to your device before they can be used in Rush. Go to the Music app to download the song.
Songs from an Apple Music subscription cannot be used because they are protected by digital rights management (see details below). In order to use songs from Apple Music, they need to be purchased.
Details about digital rights management (DRM) can be found here: Legal - Apple Media Services - Apple
Hope this helps! Let us know if you have additional questions.