In exothermic chemical reactions the combined masses of the resulting molecules is indeed slightly less than that of the inputs. But this does not make “the system’s mass appear to decrease” for two reasons. The superficial reason is that in chemical reactions the mass decrease due to energy loss from the system is far too small for us to detect, and so we did originally learn the very slightly wrong conclusion “that mass is conserved”. But the deeper reason is that, so long as the system is isolated (eg by including walls that reflect or absorb photons so that none can escape), then the system’s mass does not in fact decrease at all. This is because the system’s mass includes not just the masses of the individual molecules but also all of the energy in the system (including both photons and the thermal kinetic energy of relative motion of molecules). And if we do allow energy to escape, then the system’s mass is not conserved, as what we have learned more recently (though well over a hundred years ago now) is that what is conserved is not just the total mass of constituent particles but rather the total energy (where that includes a contribution from the masses of any particles within the system).