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We present a set of numerical-relativity binary neutron star merger simulations incorporating muons and muonic reactions for two baseline baryonic equations-of-state. In order to investigate the possible impact of muons and muonic weak reactions, we treat neutrinos with a gray (energy-independent) truncated moments scheme and an implicit-explicit time integrator. Newly computed neutrino rates are employed within the full kinematics approach for a set of relevant reactions, and pair-processes are modeled via opacities computed using reaction kernels, that allow a consistent treatment of neutrino interaction rates. We find that equilibration between matter and radiation is successfully captured by a novel two timescales approach. Of astrophysical interest is the general agreement between our muonic and nonmuonic results regarding the remnant evolution, disk and outflow properties. Average electron fractions, asymptotic velocities and temperatures are different by less than <inline-formula><mml:math><mml:mo>∼</mml:mo><mml:mn>6</mml:mn><mml:mo>%</mml:mo></mml:math></inline-formula>, while the main impact of muons is a reduction in ejecta masses by at most <inline-formula><mml:math><mml:mo>∼</mml:mo><mml:mn>17</mml:mn><mml:mo>%</mml:mo></mml:math></inline-formula>. Therefore, based on our findings, accounting for the presence of muons and muonic reactions might result much less severe consequences regarding nucleosynthetic yields and electromagnetic counterparts than previously reported in the literature.