The bug

Since snapshot 13w47c, Minecraft has support for native fullscreen (using the green button in the title bar) on macOS; a later update also allowed control+command+F to toggle this. However, Minecraft's built-in fullscreen mode, accessible through video settings or by pressing the F11 key (possibly with fn or ctrl also held down; see also MC-268226), can be toggled independently of this. Toggling these two features in a certain order can lead to the Minecraft window being black, blurry, unresponsive, without a title bar, partially split into a separate "java" window, and/or otherwise glitched.

How to reproduce

1. Launch the game. Disable Minecraft fullscreen if it is enabled.
2. Activate native fullscreen.
3. Activate Minecraft fullscreen. The Minecraft window switches to a desktop space and blocks out the other content, deactivating native fullscreen in the process; this is as expected.
4. Reactivate native fullscreen using ⌘⌃F. Visually, nothing will happen.
5. Deactivate Minecraft fullscreen. You may need to try this a few times. The screen may have visual glitches. (In some cases these can be fixed by switching to another application and back.)
6. Play around a bit more. See if you can get the Minecraft window to a similar state as in the screenshots below. If you get a window which is partially black or blurry, activate Mission Control (F3); you can see that the black/blurry bit is a separate window called "java".