No, you cannot stain plastic molding in the traditional sense, as plastic is non-porous and won't absorb liquid wood stains the way wood does.
However, you can achieve a stained or wood-like appearance using gel stains, glazes, or specialized faux-finishing techniques on many types of plastic molding (such as PVC, resin composites, or vinyl trim)
Why Traditional Staining Doesn't Work
Wood stains penetrate porous surfaces to color the material from within, but plastic resists penetration, causing the stain to sit on the surface, wipe off easily, or dry unevenly.
Even after sanding to roughen the surface, standard oil- or water-based wood stains won't adhere well or mimic natural wood grain.