  In very dense environments, neutrinos can undergo fast flavor conversions on
scales as short as a few centimeters provided that the angular distribution of
the neutrino lepton number crosses zero. This work presents the first attempt
to establish whether the non-negligible abundance of muons and their
interactions with neutrinos in the core of supernovae can affect the occurrence
of such crossings. For this purpose we employ state-of-the-art one-dimensional
core-collapse supernova simulations, considering models that include
muon-neutrino interactions as well as models without these reactions. Although
a consistent treatment of muons in the equation of state and neutrino transport
does not seem to modify significantly the conditions for the occurrence of fast
modes, it allows for the existence of an interesting phenomenon, namely fast
instabilities in the $\mu-\tau$ sector. We also show that crossings below the
supernova shock are a relatively generic feature of the one-dimensional
simulations under investigation, which contrasts with the previous reports in
the literature. Our results highlight the importance of multi-dimensional
simulations with muon creation, where our results must be tested in the future.
