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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 ALMA Band 3 (97.5 GHz) observations of GRB 171205A taken $\approx5.19$ 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 re-analyze and evaluate the archival ALMA data, we uncover systematics in the polarization calibration at the $\approx0.09\%$ level. We derive a 3$σ$ upper limit on the linearly polarized intensity of $P<97.2~μ$Jy, corresponding to an upper limit on the linear fractional polarization of $Π_{\rm L}<0.30\%$, 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 $\approx0.1\%$ level from typical radio afterglows.