  Paramagnetic point defects in solids may exhibit a rich set of interesting
and not yet fully resolved physics. In particular, character of wavefunctions
and electron-phonon coupling in these defects may highly influence their
interaction with external magnetic fields. Complex interplay between the
electronic orbitals, phonons and electron spin determines the effective
pseudospin of the system that we demonstrate on vanadium and molybdenum defects
in hexagonal silicon carbide (SiC) by means of \textit{ab initio} calculations.
In this Rapid Communication, we find a giant anisotropy in the $g$-tensor of
these defects with Kramers doublet spin ground state, resulting in reduced and
vanishing interaction with the magnetic field in parallel and transverse
directions, respectively. The consequences of our finding in the application of
these defects for quantum information processing are briefly discussed.
