  Observations of the high redshift universe provide a promising avenue for
constraining the nature of the dark matter (DM). This will be even more true
with the advent of the James Webb Space Telescope (JWST). We run cosmological
simulations of galaxy formation as part of the Effective Theory of Structure
Formation (ETHOS) project to compare high redshift galaxies in Cold (CDM) and
alternative DM models which have varying relativistic coupling and
self-interaction strengths. The interacting DM scenarios produce a cutoff in
the linear power spectrum on small-scales, followed by a series of "dark
acoustic oscillations". We find that DM interactions suppress the abundance of
galaxies below $M_\star \sim 10^8\,M_\odot$ for the models considered. The
cutoff in the power spectrum delays structure formation relative to CDM.
Objects in ETHOS that end up at the same final masses as their CDM counterparts
are characterised by a more vigorous phase of early star formation. While
galaxies with $M_\star \lesssim 10^6\,M_\odot$ make up more than 60 per cent of
star formation in CDM at $z\approx 10$, they contribute only about half the
star formation density in ETHOS. These differences diminish with decreasing
redshift. We find that the effects of DM self-interactions are negligible
compared to effects of relativistic coupling (i.e. the effective initial
conditions for galaxy formation) in all properties of the galaxy population we
examine. Finally, we show that the clustering strength of galaxies at high
redshifts depends sensitively on DM physics, although these differences are
manifest on scales that may be too small to be measurable by JWST.
