Thermal rate constants and kinetic isotope effects (KIE) for the prototypical water-forming D₂ + OH → D + DHO reaction are calculated for temperatures between 150 K and 1000 K using rigorous quantum dynamics simulations including all degrees of freedom. Very good comparison with experimental results is found for the thermal rate constants and overall good comparison with experimental KIE is obtained. Thermal rate constants and KIE for temperatures above 300 K are obtained with rigorous close-coupling calculations and employing the J-shifting approximation for overall rotational motion. Very good agreement is found validating the J-shifting approximation for this reaction. Thermal rate constants and KIE below 300 K are thus only obtained employing J-shifting. Good comparison with approximate methods for the calculation of thermal rate constants is found. The KIE for the title reaction increases notably below 250 K, which is found to be mostly due to an increased tunneling contribution in the H₂ + OH reaction at these temperatures. Furthermore, microcanonical rates are obtained which can serve as benchmarks for the further development of approximate rate constant calculations.