It depends, though, doesn't it?
I don't think that "being supportive of women" at work necessarily means that I should support their suggestions, opinions or take on things in general. Because sometimes I happen to think that a woman colleague's opinion on a given subject matter is plain wrong. Or not constructive. Or, in a single particular case for me personally, I just plain don't like her.
To me, supporting other women at work, however, very much does mean defending their right to be wrong, mediocre at what they do, annoying or just generally horrible people to the exact same extent as their male peers.
The one and only female mentor I've ever had in my life (I'm in STEM - there aren't that many of us, to begin with, and it gets worse as you rise up the ranks) once told me this: brilliant, likeable, hard-working women don't have a problem even in a male-dominated field. On the contrary, we're often beloved by bosses, subordinates and peers alike. It's when it comes to women being just as annoying, mediocre and generally strenuous as many of our male peers that the true struggle for equality begins. When a marginally competent, pretty lazy woman manages to slowly but steadily rise up the ranks until she's joined the countless crappy middle-managers that everyone loves to hate, the way men of the same type have been doing for ages, then that's true equality. And I think she's spot on, still!
Long story short: I don't think we should be supporting women's opinions on the grounds that we're women in a work context. Or necessarily listen to them if we happen to think their ideas are a bit shit. We absolutely should demand that, as women, we get away with being every bit as habitually crappy as seems to be effortlessly possible for men.
Basically, the support needs to pertain not to what we say or think but to our right to still be there even if others think we're a bit crap (or at least whatever we happen to be saying is).