We study the color-magnitude red sequence and blue fraction of 72 X-ray selected galaxy clusters at z=0.04-0.07 from the WINGS survey, searching for correlations between the characteristics of the red sequence and the environment. We consider the slope and scatter of the red sequence, the number ratio of red luminous-to-faint galaxies, the blue fraction and the fractions of ellipticals, S0s and spirals that compose the red sequence. None of these quantities correlate with the cluster velocity dispersion, X-ray luminosity, number of cluster substructures, BCG prevalence over next brightest galaxies and spatial concentration of ellipticals. Instead, the properties of the red sequence depend strongly on local galaxy density. Higher density regions have a lower RS scatter, a higher luminous-to-faint ratio, a lower blue fraction, and a lower spiral fraction on the RS. Our results highlight the prominent effect of the local density in setting the epoch when galaxies become passive and join the red sequence, as opposed to the mass of the galaxy host structure.