  We contrast predictions for the high-redshift galaxy population and
reionization history between cold dark matter (CDM) and an alternative
self-interacting dark matter model based on the recently developed ETHOS
framework that alleviates the small-scale CDM challenges within the Local
Group. We perform the highest resolution hydrodynamical cosmological
simulations (a 36~Mpc$^3$ volume with gas cell mass of
$\sim10^5\mathrm{M}_{\odot}$ and minimum gas softening of $\sim180$~pc) within
ETHOS to date -- plus a CDM counterpart -- to quantify the abundance of
galaxies at high redshift and their impact on reionization. We find that ETHOS
predicts galaxies with higher ultraviolet (UV) luminosities than their CDM
counterparts and a faster build-up of the faint end of the UV luminosity
function. These effects, however, make the optical depth to reionization less
sensitive to the power spectrum cut-off: the ETHOS model differs from the CDM
$\tau$ value by only 10 per cent and is consistent with Planck limits if the
effective escape fraction of UV photons is 0.1-0.5. We conclude that current
observations of high-redshift luminosity functions cannot differentiate between
ETHOS and CDM models, but deep JWST surveys of strongly-lensed, inherently
faint galaxies have the potential to test non-CDM models that offer attractive
solutions to CDM's Local Group problems.
