You can do this, although you still need a datastructure that allows you to use the contained type:

{-# LANGUAGE GADTs #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE TypeSynonymInstances #-}
module Tutorial where

data Gender = Male | Female deriving (Show)

data Race = White | Black deriving (Show)

type Age = Int

data Answer a where
  Answer :: RacistAgistSexist a => a -> Answer a

deriving instance Show w => Show (Answer w)

data GenderRaceAge
  = Gender Gender
  | Race Race
  | Age Age

class RacistAgistSexist a where
  genderRaceAge :: a -> GenderRaceAge
instance RacistAgistSexist Gender where
  genderRaceAge = Gender
instance RacistAgistSexist Race where
  genderRaceAge = Race
instance RacistAgistSexist Age where
  genderRaceAge = Age