Materials with tunable infrared refractive index changes have enabled active metasurfaces for novel control of optical circuits, thermal radiation, and more. Ion‐gel‐gated epitaxial films of the perovskite cobaltite La1−xSrxCoO3−δ (LSCO) with 0.00 ≤ x ≤ 0.70 offer a new route to significant, voltage‐tuned, nonvolatile refractive index modulation for infrared active metasurfaces, shown here through Kramers–Kronig‐consistent dispersion models, structural and electronic transport characterization, and electromagnetic simulations before and after electrochemical reduction. As‐grown perovskite films are high‐index insulators for x < 0.18 but lossy metals for x > 0.18, due to a percolation insulator‐metal transition. Positive‐voltage gating of LSCO transistors with x > 0.18 reveals a metal‐insulator transition from the metallic perovskite phase to a high‐index (n > 2.5), low‐loss insulating phase, accompanied by a perovskite to oxygen‐vacancy‐ordered brownmillerite transformation at high x. At x < 0.18, despite nominally insulating character, the LSCO films undergo remarkable refractive index changes to another lower‐index, lower‐loss insulating perovskite state with Δn > 0.6. In simulations of plasmonic metasurfaces, these metal‐insulator and insulator‐insulator transitions support significant, varied mid‐infrared reflectance modulation, thus framing electrochemically gated LSCO as a diverse library of room‐temperature phase‐change materials for applications including dynamic thermal imaging, camouflage, and optical memories.