If the selected key is displayed in blue, then a Transition Curve Preset has been applied which prevents it from being modified. The Transition Curve Preset must be set to Default in order to be manipulated (Curve Editor > Curve > Transition Curve Presets > Default).

However, if you would like to preserve the current Transition Curve Preset, you can use the Sample Selected Preset Curve function to resample the curve into keyframes and perform Optimize Selected to get a cleaner curve:
Curve Editor > Curve > Transition Curve Presets > Sample Selected Preset Curve.
Curve Editor Menu > Optimize > Optimize Selected.