One way to apply filters to multiple states is by onion skinning. It basically makes all objects clickable at once, regardless of what states they're on.
- Click on the small button in the lower left corner of the States panel. Make sure that "No Onion Skinning" is unchecked, and "Multi-State Editing" is checked. Also, if you want to apply the effect to all of your states, check "Show All States" as well.
- Now, while you are in the first state of animation, switch to the Select Behind tool (hit 0 to toggle from the regular selection tool). Hold down Shift and repeatedly click on the canvas to select objects from consecutive states. You can check if it works by looking at the radio buttons on the rightmost side of each state in the States panel. With each click, the radio button in the next state gets marked.
- When you're done with the selection, set the live filter as you normally would with a single object, and it will automatically apply to all selected objects in all states.
It's still a tedious method when there are a lot of objects involved, like in your case. Not only it's a lot of individual selections, but also rapid clicking will be registered as a double-click, changing the Select Behind tool to one of the marquee tools.
There might be a more efficient way, but it requires some experience with blend modes. The steps are the following:
- Make a new layer, right-click it and select "Share Layer to States". Make sure that this layer is the topmost layer in the stack.
- Draw a rectangle with solid fill, no stroke. Make sure it that it spans the entire animated area.
- With the rectangle selected, play around with the Blend modes (in the upper left corner of the Layers panel), until you get the color effect you're looking for. The color change will affect the entire animation, just as if you applied a color fill to all objects. The final look will depend on the rectangle's initial color, the blend mode, and the colors of the underlying objects.