What I find interesting is that the fandom as a whole seems to have decided that the Machine is female, Ernest Thornhill notwithstanding. Like you said, Root is the only one to use a feminine pronoun for the Machine, but fans refer to the Machine as she and her all the time, and sometimes as daddy's little girl (which, let's be honest, even if the Machine IDs as completely 100% male, it's still daddy's little girl).

I wonder sometimes if the Machine itself approaches gender as another lens of human interaction. So she interacts with Root and Harold as female (because daddy's little girl), but with John, he interacts as male (Ernest Thornhill) because he feels John interacts more with men, and with people who wouldn't care at all (eg Shaw), it would interact as whatever it damn well felt like interacting as.