When you apply brakes on a motorcycle the inertia causes the center of gravity of the motorcycle to shift towards the front. The front suspension comes into play and a good and consistent system can save or take your life. We all know most of the accidents happen not while one is accelerating but mostly when one is braking.
So my friend it is important...... using non hydraulic fluids in the forks is a safety hazard. Non hydraulic fluids such as white oil which you mentioned do not have anti foaming agent and will foam up on vigorous use..... this foaming result in a inconsistent system.
ATF and brake oil both are hydraulic fluids.