For example, in hexagonal closed-packed (HCP) structure, the atoms may be arranged in ABAB stacks or ACAC stacks. Can these two be considered enantiomers? Do they possess different solid state properties?
There are some crystal structures where the nature of the crystal structure creates chirality and therefore optical activity.
A trivial example (important because of its history: it was involved in the discovery of optical activity and molecular chirality) is tartaric acid. But the crystal is chiral because the molecule is chiral so that might not be what yyou were looking for.
But there are examples of crystals where the structure as a whole is chiral but the building blocks are not. Quartz, for example, is formed from a network of linked SiO4 tetrahedra (not molecules but a giant interlinked network where each oxygen is shared between two silicons). The overall crystal structure, though, is chiral due to small shifts in the rotation of the linked tetrahedra (see wikipedia for a detailed explanation).
I think this is a crystal analogy to molecular chirality.
Only a few crystal structures can do this and the ones you use as examples can't.
Typically, different ways of arranging atoms in a solid are referred to as phases. For a single composition, a material may have different phases depending on temperature or pressure. Different crystal structures are not referred to as enantiomers. For an HCP metal, there is no difference an ABAB stacking and ACAC stacking, other than the naming. If the stacking is ABCABC, then you have a face-centered cubic structure (FCC), not an HCP. The best way to alter solid-state properties such as resistivity, susceptibility, etc., is to change the temperature or introduce defects into the system.