No, it’s not possible, if you think about how a filter works. A filter on an object, a Sprite e.g., does its job by taking the whole of the Sprite, rendering it to a Texture, then applying the filter (or filters in a FilterChain) to that Texture.
There is no mechanism to exclude certain objects and it makes no sense to do so as that is how that container’s contents are being drawn, the only way they appear on screen. If you exclude certain objects by setting their visible to false they just won’t be drawn.
The only way to do it would be to remove it from that container and add it to another, and only apply the filter to the first container. If you make the containers otherwise identical, so with the same position, scale and orientation, then they will be drawn in the same spot and the object will be in the same place. This is a very efficient way to do it as Sprite containers are very lightweight.
The other possibility, though it would be more work, would be to apply the filter to each object so you can turn it on and off. To do this without hammering performance you could implement the filter as a MeshEffect and MeshStyle. But this would not work for all kinds of filters and would be even more work.