Problem

Even though a shortcut for Search Everywhere or Run Anything was changed in the IDE keymap settings:

these features still being triggered after performing Ctrl + Ctrl or Shift + Shift shortcuts

Solution

Go to Settings | Advanced Settings , and enable Disable double modifier key shortcuts

Notice that currently there is no way to disable only Ctrl + Ctrl or Shift + Shift separately, but there is a related feature request Allow disabling all double-control/shift/something key shortcuts individually