I couldn't find a 'Hide Backgrounds' button under Settings, so I made a small program that will temporarily rename all .jpg and .png files in your Songs folder. It effectively removes all backgrounds and beatmap skins from Osu so you can play in public without having to worry about people seeing your loli collection.
https://github.com/Tripletth/OsuHide
Binary is pushed under bin/Release.
https://github.com/Tripletth/OsuHide
Binary is pushed under bin/Release.