Polarization measurements of gamma-ray burst (GRB) afterglows are a promising means of probing the structure, geometry, and magnetic composition of relativistic GRB jets. However, a precise treatment of instrumental calibration is vital for a robust physical interpretation of polarization data, requiring tests of and validations against potential instrumental systematics. We illustrate this with Atacama Large Millimeter/Sub-millimeter Array (ALMA) Band 3 (97.5 GHz) observations of GRB 171205A taken ≈5.19 days after the burst, where a detection of linear polarization was recently claimed. We describe a series of tests for evaluating the stability of polarization measurements with ALMA. Using these tests to reanalyze and evaluate the archival ALMA data, we uncover systematics in the polarization calibration at the ≈0.09% level. We derive a 3σ upper limit on the linearly polarized intensity of P < 97.2 μJy, corresponding to an upper limit on the linear fractional polarization of ΠL < 0.30%, in contrast to the previously claimed detection. Our upper limit improves upon existing constraints on the intrinsic polarization of GRB radio afterglows by a factor of 3. We discuss this measurement in the context of constraints on the jet magnetic field geometry. We present a compilation of polarization observations of GRB radio afterglows, and demonstrate that a significant improvement in sensitivity is desirable for eventually detecting signals polarized at the ≈0.1% level from typical radio afterglows.