Why is the nose landing gear of a Rutan Vari Eze up during parking?
For getting in, the nose has to be physically raised before the pilot can board the aircraft:

When the aircraft is parked, the NLG is retracted and the aircraft rests on the bumper at the front of the aircraft, in what is described as the 'kneeled' position.
Extension of the NLG requires the front of the aircraft to be physically raised, after which the NLG extension system is operated from the cockpit.
To begin the NLG extension, a handle in the cockpit is turned in he extend direction. This handle is connected to a shaft that turns a worm gear and crown wheel, and the rotation of the crown wheel drives the actuating rms of the NLG in the down direction.  When the NLG is extended, an extra 1.5 turns of the handle causes the crown wheel to drive the actuating arms over-centre, which locks the gear in the fully down position.

After this, the pilot boards the aircraft. On some aircraft, linear actuators seems to have been fitted for this purpose:

In recent years the application of general purpose, 12 volt, linear actuators came into use for electrical actuation of the nose gear with the airplane loaded.
With the linear actuator the airplane can be parked nose down for stability, boarded (in the nose down position) and raised by the push of a button.

As noted above, this design has been adopted for stability- As the engine is on the rear, if the pilot is not in the aircraft, it can tip backwards, damaging the propeller. This also acts as a parking brake.