Reply #7: I think the description of her Maude character is quite accurate and fair:

[Berry Cool]

"An unabashed liberal, a bit of a loudmouth and a tough broad with a soft heart, she was, in the parlance of the time, a liberated woman, who sometimes got herself into trouble with boilerplate biases just the way her cultural opposite number, Archie Bunker, did."

I think the term "battle-ax" is used here with a bit of implied irony. As in, Maude was certainly a contentious soul, and so was Dorothy for that matter--but not a nasty one. Just one who stubbornly and loudly defended her beliefs--and was sometimes wrong about things.