Do pilots allow for Earth's rotation when navigating?

It depends on the method of navigation. The motion of a ship or aircraft is relative to the earth, so inertial navigation or navigation by dead reckoning do not have to take the Earth's rotation into account. Similarly, if the pilot of a ship or aircraft is navigating by visible points of reference or by terrestrial radio beacons, then the rotation of the Earth does not have to be taken into account.

However, if the pilot is relying on celestial navigation, then the rotation of the earth must be taken into account, because the stars are being used as a frame of reference. Similarly, if the navigation relies on GPS, the GPS system must include the rotation of the Earth in its calculations, as the orbital planes of the GPS satellites are aligned to distant stars and do not move with the rotation of the Earth.