For many years the standard explanation for blue jay blue was that it was produced by scattering, the same process that makes the sky blue. In the jay, the cells containing these microscopic particles are underlain by another cell layer containing the dark pigment melanin. The contrast of blue against a dark background makes the color stand out. In parrots you've got the same basic structure, except that the blue-producing layer is overlain by a transparent yellow layer. Blue masked by yellow produces green.
White feathers are also schemochromic.
They look that way because they reflect all colors, but they contain no pigment and under certain conditions can be shown to be transparent. Fine, you say. The phenomenon here is called interference or coherent scattering. Basically, as light bounces off the regularly spaced microscopic structure of the feather, it splits and then recombines. When it does so, all the wavelengths cancel out except blue, which intensifies.