This is a limitation both of Forest Pack and how GPU render engines work:
Some features (as Forest Color/Forest Edge) need to be implemented at rendering time.
That means we must write a specific piece of code (different for each renderer), which applies these features when scene is rendering.
For CPU renderers, this can be done if the render provides a SDK (developer kit), with support for third-party plugins (i.e. V-Ray or Arnold).
But usually this possibility is not available for GPU renderers, for several reasons. So, we have not way to implement it.
Regarding animated objects, this is not a render time feature, and (usually) can be implemented both for CPU/GPU.
But except in V-Ray or Arnold, this must be implemented by the renderer developers, using the information provided by the Forest API.
What is your render engine ?