We control a Conspiracy with chosed creature type Anteater. On a draw step we draw a Mirror Entity, and play it on main phase.
Wich creature type it has:
- in hand?
- in stack?
- on battlefield?

The Mirror Entity is an Anteater (and only an Anteater) in all three zones.

Both Conspiracy's ability and Changeling are type-changing effects that are applied in layer 4, but Changeling is a characteristic-defining ability and so will always be applied first. Afterwards, Conspiracy comes along and overwrites the Entity's type, turning it into just an Anteater.