The same will happen with any recording software if you select to capture the Monitor but run a fullscreen game. Fullscreen games can only be captured by a game-capture like implementation that hooks into opengl, directx or whatever the game is using.
You might want to try to run OBS as an administrator and then try capturing Minecraft with game capture while running Minecraft in window mode (if Minecraft is minimized it will probably not render so your screen might stay black in OBS, thats why I would recommend to use window mode first and then later go fullscreen). If game capture is not working for some reason you can post a log and we can take a look at what the reason might be.
I normally try to do a quick test recording of just running the game, capturing it, testing my voice input etc. If everything works fine I then start the real recording.
