Force on the dipole is \(\overrightarrow{ F }=(\overrightarrow{ p } \cdot \vec{\nabla}) \overrightarrow{ E } \equiv 0\) always in this case.

Torque on the dipole \(\vec{\tau}=\overrightarrow{ p } \times \overrightarrow{ E }\)

if the dipole moment and the electric field are parallel to each other, then the torque may be zero because \(pE \sin 0=0\)