If she was a guy, I doubt anyone would suggest her ineptitude was gender-based, but instead dumbass-based.
I don't think I have seen problems with her coming down to her being a woman really. A writer/showrunner accused of being a crap writer/storyteller or being tunnel-visioned for having a bias towards a certain character/actor is something that happens both to men and women IMO. Al/Miles of Smallville-fame pretty much got the same accusations for Lanaville that Gamble has gotten. Or that David Shore of House has gotten for the 13-character. And that hasn't been all that different from the criticism Marti Noxon has gotten back in the day for all-Spike-all-the-time.
From what I've seen right now people seem open to Carver because he wrote some good episodes on Supernatural, produced a show that is considered not that bad (can't comment on it as I haven't seen it) and you can't really predict if he'll favour one character above all others.
Say, hypothetically, another former or current writer was announced as showrunner. Like Raelle Tucker. Now she left a lot longer ago but I personally enjoyed her episodes. In fact, I think, in hindsight, I have to say the episodes she and Gamble wrote together, Tucker brought the good stuff in. So, I consider her a good writer and would welcome her. And I believe she wouldn't be met with absolute hatred by most of fandom either.
Julie Siege on the other hand? In the end I was really glad to see her go.
Or take a man, if John Shiban came back, it might look really weird but I wouldn't guess a "noooooooo" reaction to it either.