  We study the linear stability of a planar interface separating two fluids in
relative motion, focusing on the symmetric configuration where the two fluids
have the same properties (density, temperature, magnetic field strength, and
direction). We consider the most general case with arbitrary sound speed
$c_{\rm s}$, Alfv\'en speed $v_{\rm A}$, and magnetic field orientation. For
the instability associated with the fast mode, we find that the lower bound of
unstable shear velocities is set by the requirement that the projection of the
velocity onto the fluid-frame wavevector is larger than the projection of the
Alfv\'en speed onto the same direction, i.e., shear should overcome the effect
of magnetic tension. In the frame where the two fluids move in opposite
directions with equal speed $v$, the upper bound of unstable velocities
corresponds to an effective relativistic Mach number $M_{re} \equiv v/v_{\rm
f\perp} \sqrt{(1-v_{\rm f\perp}^2)/(1-v^2)} \cos\theta=\sqrt{2}$, where $v_{rm
f\perp}=[v_A^2+c_{\rm s}^2(1-v_A^2)]^{1/2}$ is the fast speed assuming a
magnetic field perpendicular to the wavevector (here, all velocities are in
units of the speed of light), and $\theta$ is the laboratory-frame angle
between the flow velocity and the wavevector projection onto the shear
interface. Our results have implications for shear flows in the magnetospheres
of neutron stars and black holes -- both for single objects and for merging
binaries -- where the Alfv\'en speed may approach the speed of light.
