We experimentally studied the viscous fingering instability considering a Newtonian oil displacing viscoelastic shear-thinning liquids and vice versa. The non-Newtonian liquids are aqueous solutions of polyacrylamide and xanthan gum, i.e., flexible and rigid polymers, respectively. A rectangular Hele-Shaw cell, connected by two plenum chambers, was developed to evaluate the displacement of a fixed volume. The experiment consists of analyzing the interface time evolution through a digital camera as a function of the geometric, dynamic, and rheological parameters. The displacement efficiency was determined through image processing in order to identify the formation of fingers or plugs. Unlike the Newtonian case, the transition does not occur when the viscosity ratio is roughly equal to one, but nevertheless, it was observed that the stability of the interface depends on the viscosity ratio. Specifically, more branches are observed at low viscosity ratios. Furthermore, a higher stability is observed when the Newtonian liquid displaces the shear thinning liquid, especially when the polymer is more rigid. When the Newtonian liquid is being displaced, elastic effects favor the displacing efficiency.