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We present a classification of Kerr-de Sitter spacetimes based on the presence of horizons, ergospheres, and the characteristics of photon motion. We utilize the concept of local escape cones for isotropically radiating point sources to create shadows of the Kerr-de Sitter naked singularities within a class containing astrophysically relevant parameters. For completeness, we also consider in the construction photons entering the region of negative radii of the naked singularity spacetimes. The shadow construction is associated with two astrophysically significant families of local reference frames (or local observers). The first family represents locally nonrotating frames that, near the so-called static radius in Kerr-de Sitter spacetimes, exhibit characteristics similar to those of static observers at large distances in asymptotically flat spacetimes. The second family involves radially escaping geodesic frames, which are suitable for constructing the shadow near the cosmological horizon of Kerr-de Sitter spacetimes. We explore how the aberration effect, caused by the motion of free observers due to the repulsive influence of the cosmological constant, modifies the shadow in comparison to those related to stationary locally nonrotating observers.