DialogMusicPlayer appDialogMusicPlayer is Multimedia tool that is open source under the GPL-3.0-only license. The stock music player on my phone needed unnecessary permissions! So, I created one on my own :D
Dialog Music Player is the most minimalistic music player requiring no permissions except to access your storage (so that it can play your music).
Do not be irritated if you don't find a launcher icon: there currently is none. The app accepts music files to play via the "open with" menu or from the "share to" menu of Android, e.g. via a file manager, other utility apps etc. And as it has no icon in the launcher: should you ever want to uninstall it, you'll have to do that via Android's Settings › Apps menu (or via the „market app“ you used to install it).