The first measurement of the temperature of the hydrogen 21-cm signal reported by EDGES strongly favors the Coulomb-like interaction between freeze-in dark matter and baryon fluid. We investigate such dark matter in both the one- and two-component context with the light force carrier(s) essential for the Coulomb-like interaction being other than photons. Using a conversion of cross sections used by relevant experiments and Boltzmann equations to encode the effects of the dark matter-baryon interaction, we show that both cases are robustly excluded by the stringent stellar cooling bounds in the sub-GeV dark matter mass range. The exclusion of the one-component case applies to simplified freeze-in dark matter with the light force carrier as dark photons, gauged , ,, or axion-like particles, whereas the exclusion of the two-component case applies to simplified freeze-in dark matter with the two light force carriers as two axion-like particles coupled to standard model quarks and leptons.