  Based on extensive simulations, we conjecture that critically pinned
interfaces in 2-dimensional isotropic random media with short range
correlations are always in the universality class of ordinary percolation.
Thus, in contrast to interfaces in $>2$ dimensions, there is no distinction
between fractal (i.e., percolative) and rough but non-fractal interfaces. Our
claim includes interfaces in zero-temperature random field Ising models (both
with and without spontaneous nucleation), in heterogeneous bootstrap
percolation, and in susceptible-weakened-infected-removed (SWIR) epidemics. It
does not include models with long range correlations in the randomness, and
models where overhangs are explicitly forbidden (which would imply non-isotropy
of the medium).
