It is, in fact, supported in Tolkien's writings. She is described as "Amazon...capable of athletic feats" in one of Tolkien's last letters and in some writings she fought against Feanor at the kinslaying. There are other ways her First/Second Age character could be interpreted (as Tolkien constantly changed her backstory), but Amazon's take is a legitimate one.
The idea that Galadriel has to always be the enigmatic, wise, and serene queen of the woods is a projection backwards of the late Third Age Galadriel. It's not rooted in the texts Tolkien wrote about her younger self, even granting they're jumbled and contradictory. (It's also an incomplete reading of even her Third Age character)
That said, is it possible the showrunners will push the "brash and headstrong" angle they describe in an interview too far in a way that makes her unlikable? Sure. But most of the complaints I see aren't about that.