Well, actually, "Spirit" comes from the Latin for "To breathe" (which is also the same root behind "respiration" -- and "inspiration").

So, technically, you can still be "spiritual" without believing in anything supernatural (i.e. outside of the natural), and certainly without having to attatch any importance to any particular religious doctrine. All you have to do to fit that definition is to believe that all things that breathe (and plants breathe, too) share a connection to one another.

And technically, Animism also attribute souls to rocks and other geological formations, too -- not just plants.