Make sure the bug also happen when Details! is the only addon enabled.
CONFIRMED

Game and Details! version
Game Version: 1.14.1
Details! Version: C222

Describe the bug

• Steps to Reproduce (what did you do to make the bug happen):
  Through GUI, Options > Bars: Texts > {remove or apply text shadow}
  Through GUI, Options > Bars: Texts > {remove or apply Outline}

• Result (what happens when you follow the steps above):
  Text becomes outlined when shadow is applied - not a shadow.
  Nothing happens when outline is applied or removed, regardless of Outline Color.

• Expected (what you think the expected behavior would be when following the steps):
  When Text Shadow is enabled, apply a drop shadow then remove when it is disabled.
  When Outline is enabled, apply an outline to the text in the color from the Outline Color picker then remove when it is disabled.

• When the bug started (a date, wow path release, details update, etc)?
  This is a fresh Classic ERA install, TBC options work fine.

• Additional information:
  None

Lua Error
Post here lua errors, if you aren't getting any, use /console scriptErrors 1
None

Screenshots
Post images of the bug if necessary.

Combat Log
N/A

Other Information
If necessary, add more info here.

Can confirm this is still happening on retail too.

Text becomes outlined when shadow is applied - not a shadow.
Nothing happens when outline is applied or removed, regardless of Outline Color.

Additiional Info on that part. Outline changes the application of shadow,
but only if you tick and untick (or vice versa) the Text Shadow option afterwards.