I think what’s often going on when people say “don’t vote for a woman just because she’s a woman,” is that they’re suggesting women are less likely to be qualified for office than men. I think they’re saying that women candidates need to be examined more closely.
It’s pretty much the same thing as assuming that women who make it past the thorough vetting needed for nomination are still probably not qualified to run.
How much more sexist could you get than that? It’s discouraging.
By the way, did you know that the Air Force has discovered that women often make better candidates for fighter pilots than men?
Something to do with women reacting with more cool and less emotion during times of extreme stress.