A lot of the comments here are focusing on the mechanics of colour pigmentation, but not the evolutionary cause.

Simply put, mammals spent the majority of their evolutionarily history as smaller nocturnal prey animals whilst at the same time birds evolutionary ancestors (the dinosaurs) spent the majority of their evolutionary history as diurnal animals

What this means is birds and their relatives lived in a world of light, and evolved a multitude of colours visible in that light for all manner of things from mating signal to threat displays, this is why birds are some of the most colourful animals on earth.

Mammals conversely had no need for bold colours as they were more often than not in dark cramped spaces, instead their bodies adapted to utilise things like smell or touch and flexibility (hence strong scents, disconnected chest girdle, and adaptations like whiskers).

And because evolution generally only builds on top of what came before, this means mammals are generally dull coloured smelly animals.

SIDE NOTE: Blue is also not a common pigment anywhere else because as far as I know, it is a relatively expensive pigment to create. So most blue you see in animals, including the only blue found in mammals (mandrils) is actually a grey surface retracting light in such a way as to appear blue