You don't need to be registered or logged in to download songs.
Click on the Forums (globe icon) in the top left corner of the iReal Pro window.
This will open the forums in your default browser where you can choose a music genre (Jazz, Pop, Latin...)
Or Tap on Main Playlists above.
For example, to download the Jazz 1410 standards playlist, click the Jazz genre forum area.
Click the Jazz 1410 standards conversation thread.
Click on the playlist link in the post.
If you see this message, click Allow so the songs can be imported.
 Allow message for importing 
The Import Preview window will open. Click Import Playlist.
(Alternatively for any Playlist, you can click on the arrows to see each individual song in that Playlist to import one song or to see the songs it contains.)
Search the Forum information here