Hang on, so if you shine a white light through a blue filter, the light on the other side looks blue. And the filter itself still looks blue on both sides. But then, where did the non-blue component of the light go?

Imagine looking at this blue-transparent bag with a red light, it will appear more opaque.

It means some blue goes through, some is reflected.

As a guess, perhaps the unfiltered light that gets through goes through a phase change from being reflected. https://en.wikipedia.org/wiki/Reflection_phase_change