  Khovanov-Floer theories are a class of homological link invariants which
admit spectral sequences from Khovanov homology. They include Khovanov
homology, Szab{\'o}'s geometric link homology, singular instanton homology, and
various Floer theories applied to branched double covers. In this short note we
show that certain strong Khovanov-Floer theories, including Szab{\'o} homology
and singular instanton homology, are invariant under Conway mutation. This
confirms conjectures of Seed and Lambert-Cole. Along the way we prove two other
conjectures about the structure of Szab{\'o} homology.
