Combustion instability, or the coupling between flame heat release rate oscillations and combustor acoustics, is a significant issue in the operation of gas turbine combustors. This coupling is often driven by oscillations in the flow field. Shear layer rollup, in particular, has been shown to drive longitudinal combustion instability in a number of systems, including both laboratory and industrial combustors. One method for suppressing combustion instability would be to suppress the receptivity of the shear layer to acoustic oscillations, severing the coupling mechanism between the acoustics and the flame. Previous work suggested that the existence of a precessing vortex core (PVC) may suppress the receptivity of the shear layer, and the goal of this study is to first, confirm that this suppression is occurring, and second, understand the mechanism by which the PVC suppresses the shear layer receptivity. In this paper, we couple experiment with linear stability analysis to determine whether a PVC can suppress shear layer receptivity to longitudinal acoustic modes in a non-reacting swirling flow at a range of swirl numbers. The shear layer response to the longitudinal acoustic forcing manifests as an m=0 mode since the acoustic field is axisymmetric. The PVC has been shown both in experiment and linear stability analysis to have m=1 and m=-1 modal content. By comparing the relative magnitude of the m=0 and m=-1,1 modes, we quantify the impact that the PVC has on the shear layer response. The mechanism for shear layer response is determined using companion forced response analysis, where the shear layer disturbance growth rates mirror the experimental results. Differences in shear layer thickness and azimuthal velocity profiles drive the suppression of the shear layer receptivity to acoustic forcing.