This is probably an ok use for a GADT. Something like:

{-# LANGUAGE DataKinds      #-}
{-# LANGUAGE GADTs          #-}
{-# LANGUAGE KindSignatures #-}

data Bap = Baptized | Unbaptized

data Person :: Bap -> * where
   Baptize :: Person Unbaptized -> Person Baptized
   NewPerson :: Person Unbaptized

conditionalBaptize :: Person a -> Person Baptized
conditionalBaptize p =
    case p of NewPerson -> Baptize p
              Baptize _ -> p

main = return ()

It looks pretty normal to me as a professional Haskeller, though I suppose it's perhaps slightly cleaner to write it as conditionalBaptize p = fromMaybe p $ baptize p. It's largely just a matter of taste and I'd accept either version when reviewing an MR.

Edit: I just thought of another version that actually is far too clever and shouldn't be used:

conditionalBaptize = ap fromMaybe baptize, making use of the monad instance for ->. But yeah, don't do this.