Can a naked Changeling use its Shapechanger feature to duplicate the appearance of clothing or equipment, similarly to Mystique from the X-Men?
As an action, you can change your appearance and your voice. You determine the specifics of the changes, including your coloration, hair length, and sex. You can also adjust your height and weight, but not so much that your size changes. You can make yourself appear as a member of another race, though none of your game statistics change. You can’t duplicate the appearance of a creature you’ve never seen, and you must adopt a form that has the same basic arrangement of limbs that you have. Your clothing and equipment aren’t changed by this trait. You stay in the new form until you use an action to revert to your true form or until you die.
The feature states that it can’t change your clothing and equipment, but doesn’t mention anything regarding changing your body to duplicate the appearance of clothing or equipment.
It also states that you can turn into other races. So if a Changeling can turn into, for example, a Yuan-ti Pureblood and duplicate the appearance of scales, then I see no reason why it wouldn’t be able to duplicate the look of leather, or silk, or other clothing materials.
