For an unknown reason, textures containing transparency information do not render correctly when applied to Crowd Characters while they appear fine on the source Character. Even if we did not really understood the underlying reason, there is a easy workaround.
Difference between source material and crowd-applied material
It's needed to enable the Refractions attribute in the Raytrace Options panel of the shader:
And the resulting rendering:
Result with Refractions set to On