  Motivated by the recent discovery of odd-parity multipolar antiferromagnetic
order in CeRh$_2$As$_2$, we examine the coexistence of such translation
invariant Kramers' degenerate magnetic states and superconductivity. We show
that the presence of such magnetic states generically suppresses
superconductivity, whether it be spin-singlet or spin-triplet, unless the
magnetic state drives a symmetry-required pair density wave (PDW)
superconducting order. We apply our results to CeRh$_2$As$_2$, where no pair
density wave order appears; and to the loop current order in the cuprates,
where such pair density wave superconductivity must appear together with
Bogoliubov Fermi surfaces. In the former case, we explain why superconductivity
is not suppressed.
