Easily possible. I think I can describe a passive system that could accomplish this.
But first: Tut, tut. Inverted footprints on grass would be magenta (purplish), not red! Color theory matters!
Consider the three following hypothetical fluorescent substances:
- A red-absorbing substance which fluoresces cyan.
- A blue-absorbing substance which fluoresces yellow.
- A green-absorbing substance which fluoresces magenta.
[These are the "opposite" colors for the typical human eye, as a matter of basic biology (not physics!). Learn them, love them, and mock the crap out of any art teacher who tries to teach otherwise.]
Each of these absorb and fluoresce over a range, not just a specific frequency (pair of frequencies, for magenta), carefully chosen to match the human eye.
Each of the substances take the light on one side, and shine it out the other side. So if they are on a green leaf, and white sunlight comes in, they absorb RGB white light, and shine CMY white light down onto the leaf. The leaf reflects mostly green (from the yellow + cyan overlap), which is absorbed only by the magenta-emitting material.
The overall effect is that, when these three materials together are sprayed on a green thing, it glows magenta.
This gets you the color-wheel hue-flipping fairly easily, without needing any kind of context-sensitive chemicals.
Tetrachromats, the colorblind and others will not really see the illusion correctly, but then, they won't see it correctly however you flip it. Their eyes work differently, they don't have the same primary colors.
There's still the problem that the brightness needs flipping too.
Since the above relies on a light-path through the three filters to the leaf and back again, we have made this task much simpler, as if it flips indiscriminately, it will flip from light to dark and back, as the light goes through and back.
But what if the metamaterial polarizes itself? The particles are charged. They align by consensus: each particle aligns to the average of its neighbors. Rapidly, pockets of similarity emerge, and the whole pool snaps to a single polarization, like throwing a handful of small magnet-beads into a bowl.
Now each particle blocks all "vertically-polarized" light (where "vertical" is defined as whatever average alignment the particles locally have agreed to align with).
And each one rotates the polarity of the light going through it by an angle from zero to 45 degrees, depending on the intensity of the light it is absorbing.
At the brightest light, light enters the filter layer, is flipped to its inverse color and rotated 45 degrees, is reflected back, flipped 45 degrees again, and so has been rotated 90 degrees and does not get through.
In the dimmest light, it gets rotated zero degrees coming in, and zero again on the return path.
That takes care of it darkening in bright light.
But what about glowing in dark light?
Well, that's the speciality of fluorescence!
Personally, I'd just skip the "darkening in bright light" thing (it's not part of the spec, explicitly, except that white should probably turn dark. Screw that, just have white turn WHITER!).
Instead, let's have our three original substances all also absorb non-visible wavelengths like UV and IR, and fluoresce them at their chosen output wavelengths.
Then the footsteps will always glow the opposite hue:
- black -> light-grey.
- white -> bright white.
- brown/beige/skintone -> shades of blue.
To find which color you'd see, go to your favorite image editor (or image editing website), invert the hue (Shadows and highlights should not flip, only the hue!), then increase the brightness a little.