Looking at the Wikipedia page https://en.wikipedia.org/wiki/Rep-tile all examples of rep-tiles that are not polygons have fractal boundaries.
In general, if the Hutchinson attractor of an IFS of similitudes is not a polytope (or apeirotrope), is it's boundary fractal?
The four corner set $K$ (which is a Cartesian square of the middle half Cantor set) has an empty interior (so it coincides with its boundary) and has Hausdorff dimension 1. The set $K$ is self-similar, as it is a union of four images $f_i(K)$ by contracting similarity maps.