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JWST has revealed a large population of compact, red objects at z > 4 known as Little Red Dots (LRDs). We analyze the spectral energy distributions (SEDs) of 88 LRDs from the JWST PRIMER survey with complete photometric coverage from 1 to 18 μm using NIRCam and MIRI imaging, representing the most extensive SED analysis on a large LRD sample with long-wavelength MIRI data. We examine SED models in which either galaxy or active galactic nucleus (AGN) emission dominates the rest-frame UV or optical continuum, extracting physical properties to explore each scenario’s implications. In the galaxy-only model, we find massive, dusty stellar populations alongside unobscured, low-mass components, hinting at inhomogeneous obscuration. The AGN-only model indicates dusty, luminous AGNs with low hot dust fractions compared to typical quasars. A hybrid AGN and galaxy model suggests low-mass, unobscured galaxies in the UV, with stellar mass estimates spanning ∼2 dex across the different models, underscoring the need for caution in interpreting LRD stellar masses. With MIRI photometry, the galaxy-only model produces stellar masses within cosmological limits, but extremely high stellar mass densities are inferred. The hybrid model infers highly overmassive black holes exceeding those in recently reported high-redshift AGNs, hinting at a partial AGN contribution to the rest-optical continuum or widespread super-Eddington accretion. Our findings highlight the extreme conditions required for both AGN- and galaxy-dominated scenarios in LRDs, supporting a mixed contribution to the red continuum, or novel scenarios to explain the observed emission.