In optical testing, the well-known peak valley detection ambiguity exhibited by degenerate interference intensity patterns is due to phase. The interplay between phase and polarization is evident in coherence theory. So the theme of intensity degeneracy arising due to polarization is taken up in this article for discussion. Fringes with high contrast (visibility) occur when the interfering beams are in same state of polarization (SOP). But when multiple beams are involved in interference, high contrast fringes are possible even if the SOP of each of the interfering beams is different. We show the superposition of multiple beams in different SOPs form lattice patterns consisting of polarization singularities and the intensity distribution in the interference patterns exhibit high contrast. By changing the SOPs of the individual beams, same intensity distributions can be produced. These intensity patterns are termed as degenerate intensity patterns, but have different polarization distributions. The SOP changes must follow certain rules to achieve degenerate intensity patterns. We also demonstrate intensity degeneracies in Fraunhoffer diffraction patterns of apertures illuminated by beams having polarization singularities. This study therefore illustrates the limitations on intensity based measurements in identifying polarization singularities as these singularities are expected to play a major role in future in diverse areas of optics.