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Chemical trends for the solubility and diffusivity of hydrogen in austenitic high Mn steels have been studied employing density-functional theory. Considering the dilute limit of hydrogen, we observe strong volumetric effects of substitutional Mn and interstitial carbon on the energetics of a hydrogen atom within the lattice. This volume dependence yields a significant increase both in the solubility and the mobility of the H impurity when comparing Fe1-xMnxCy with pure Fe. By means of kinetic Monte Carlo calculations, we also show that H impurities can use Mn percolation chains as efficient diffusion channels. These trends may explain why Mn-rich steels are often observed to be more prone to hydrogen embrittlement than conventional austenitic steels.