On most Linux desktops alt+click will allow you drag a window by clicking anywhere over it. This conflicts with the multiple cursors binding.

It's still possible to obtain multiple cursors with commands like insertCursorAbove or insertCursorAtEndOfEachLineSelected, but this affects multiple people, and it's already covered in some articles with a workaround (which I'm copying here for Gnome based systems: gsettings set org.gnome.desktop.wm.preferences mouse-button-modifier "<Super>" change <Super> with your preferred key )

It's also acknowledged in VScode's documentation that this shortcut might conflict even on Windows or Macosx...

Note: Your graphics card provider might overwrite these default shortcuts.

So, fixing this for Linux users might also be useful elsewhere. For comparison, the Atom editor uses ctrl+click instead of alt+click for this shortcut.

Rather than changing the default, making it customizable would already be a welcome improvement, but afaik unfortunately there's no way to change it. These are a couple of related default keybindings:

{ "key": "ctrl+shift+up",         "command": "editor.action.insertCursorAbove",
                                 "when": "editorTextFocus" },
{ "key": "shift+alt+up",          "command": "editor.action.insertCursorAbove",
                                 "when": "editorTextFocus" }

But since I cannot find any editor.action.insertCursor command, it seems that this option is lacking.