On aircraft with powered control surfaces it doesn´t matter, but on aircraft with manually controlled elevator, negative camber of the horizontal stabilizer results in a "stick forward" zero elevator force, the faster you go, the higher the stick forward tendency, the aircraft is free-stick-instable. So basically you need to have either an S-sloped airfoil, or one with at least a positively combered elevator to make the aircraft stable. Symmetrical airfoils are neutral with that respect, all stick-free-stability comes from the fixed-stick-stability, which causs an elevator deflection over speed curve with enough gradient, to also produce enough stick force over speed gradient.
Positive camber plus trim tab may work as well, but is not very efficient. Additional springs in the elevator system may provide the desired force gradient as well.
Several gliders have symmetrical horizontal stabilizer airfoils up to the hinge but positively cambered elevators aft of that, often created by a the naturally concave surface of the laminar flow airfoil combined with an (easy to build) flat upper elevator surface.
The
Wilga even has a fixed (negative) slat on the elevator horn.