We examine the impact of the strength of the ER=127 keV, 26Al(p,γ)27Si resonance on 26Al production in classical nova explosions and asymptotic giant branch (AGB) stars. Thermonuclear 26Al(p,γ)27Si reaction rates are determined using different assumed strengths for this resonance and representative stellar model calculations of these astrophysical environments are performed using these different rates. Predicted 26Al yields in our models are not sensitive to differences in rates determined using zero and a commonly stated upper limit corresponding to ωγUL=0.0042 μeV for this resonance strength. Yields of 26Al decrease by 6% and, more significantly, up to 30%, when a strength of 24×ωγUL=0.1 μeV is assumed in the adopted nova and AGB star models, respectively. Given that the value of ωγUL was deduced from a single, background-dominated 26Al(3He,d)27Si experiment where only upper limits on differential cross sections were determined, we encourage new experiments to confirm the strength of the 127-keV resonance.