Do horizontal stabilizers on airliners have varying angle of incidence in the span-wise direction (washout or negative twist)?
There is little to be gained by twisting the horizontal stabilizer in terms of efficiency.

First, the span of a typical horizontal tail is much smaller than the wing (see A320 illustration below for example). Apart from the small outboard portions, the downwash behind most of the wing is fairly constant. This makes the simplification of a uniform downwash on horizontal tail valid.



Second, the lift and drag contribution of the horizontal tail on the overall aircraft at cruise, during which aerodynamic efficiency is paramount, is fairly small. Even assuming a large static margin of 30% (smaller static margin equates to smaller tail contribution), improving the tail span efficiency from 0.8 (typical) to 1 (elliptical) only reduced the total induced drag by half a drag count using some typical aircraft parameters.

These are the parameters I used if you want to verify yourself:


$C_{L_{trim}} = 0.4$
$\alpha_{wb} = 4.8$
$\frac{\partial\epsilon}{\partial\alpha} = 0.43$
$\epsilon_0 = 2.8$
$C_{m_{ac_{wb}}} = -0.12$
$\overline{V_H} = 0.6$
$a_t = 4$
$\frac{S_t}{S} = 0.25$
$h_{n_{wb}} = 0.22$
$C_{L_{0_{wb}}} = 0.4$
$e_{wb} = 0.85$
$e_t = 0.8$ (typical, compared to fully elliptical of unity)
$A_{wb} = 8$
$A_t = 5$