A mind flayer has the following requirement in order to perform its Extract Brain Action (MM, 222):
one incapacitated humanoid grappled by the mind flayer.
If a humanoid has been polymorphed (PHB, 266):
This spell transforms a creature that you can see within range into a new form…
The target's game statistics, including mental ability scores, are replaced by the statistics of the chosen beast. It retains its alignment and personality.
If a humanoid has used the Wild Shape class feature, they (PHB, 66-7):
magically assume the shape of a beast that [they] have seen before.
Your game statistics are replaced by the statistics of the beast, but you retain your alignment, personality, and Intelligence, Wisdom, and Charisma scores.
You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so.
In both forms, the creatures are clearly in a beast shape, but are they (or their brains) still considered "humanoid"?
Best Answer
The extraction can't be done
Both Polymorph and Wild Shape tell their target to assume the new form's game statistics, which includes (Monster Manual, page 6) the creature's type (Humanoid, Beast, Fiend, et cetera). A PC is usually humanoid, but if they use Wild Shape or Polymorph, their creature type can change.
The Mind Flayer's brain extraction action specifically targets "one incapacitated humanoid grappled by the mind flayer". Therefore, beings that are not humanoids, even temporarily, cannot be targeted by this special attack. A shapeshifter druid is therefore relatively safe when mauling against a mind flayer in bear form!