Handmaid's Tale author Margaret Atwood recently said that being a feminist doesn't mean always agreeing with everything every woman says (is that even possible?), or blindly supporting someone and their policies or beliefs just because they are a woman. Atwood specifically gave British Prime Minister Theresa May as an example of a woman she doesn't necessarily agree with.
I have to say I personally have a much better view of Theresa May. But otherwise, I do agree with Margaret Atwood. Feminism means supporting equal rights regardless of gender. It doesn't mean supporting women for the sake of supporting women.
During the Rudd-Gillard wars in Australia (2010-2013), I really didn't appreciate other feminists who thought of me as less of a feminist because I chose to support Rudd. I wasn't going to give Gillard a free pass even if she was Australia's first female prime minister. It was during this period that I started strongly rejecting the idea that feminists must always support other women. During the Clinton-Sanders wars in America (2016), I personally supported Clinton, but I didn't think it was any less feminist to support Sanders, if one's politics was more in line with his platform. I proudly stated this to my friends, both Clinton and Sanders supporters. Perhaps because some prominent feminists were Sanders supporters, or perhaps because I was already personally supporting Clinton, this time this particular stance was much more well received.
The bottom line is this: being a feminist doesn't mean putting having a female president ahead of everything else. (By the way, if that was the case, would we all need to support Sarah Palin, should she become the Republican candidate? I really hope not.)
p.s. No disrespect to Gillard. The Rudd-Gillard thing is over now, and both former PMs have handled themselves with grace after their departure from politics.