You can now officially move playlists between Apple Music and YouTube Music. Apple has published two help documents (linked to the sources below) that outline what you need to do to switch between the services.
Before you ask, no, there is no official way to switch from Apple Music to Spotify or from Spotify to Apple Music. As of now, it is only Apple Music to YouTube Music or from YouTube Music to Apple Music.
Remember that only playlists you created (including collaborative playlists you own) are transferred. Music files, non-collaborative shared playlists, and curated playlists, as well as folders where you've organized your Apple Music playlists, aren't transferred.
If an Apple Music playlist you want to transfer includes podcasts, audiobooks, or user-uploaded audio files, those won't be transferred, and only the songs in the playlists will be transferred. If the service you're transferring to doesn't offer specific songs, they obviously won't be transferred.
The entire process, regardless of direction, should usually take a few minutes, but it can take up to several hours depending on how many playlists you're transferring. Full instructions on how to transfer are available in the sources linked below.
Source 1 | Source 2