We present linearized stability analyses of the effect of slow anisotropic compression or expansion on the growth of perturbations at accelerated fluid interfaces in both planar and spherical geometries. The interface separates two fluids with different densities, compressibilities, and compression rates. We show that a perturbation of large mode number on a spherical interface grows at precisely the same rate as a similar perturbation on a planar interface subjected to the same normal and transverse compression rates.