Billary was a meme that started during the Clinton administrations to mock her for actually trying to accomplish something and not staying in her place.
It's like when people called Obama uppity, it's code. I don't think anyone using language like that is worth listening to.
I wasn't really aware of what was going on politically back then so I don't know what kind of language was being used, but if people wanted Hillary to "stay in her place" that could mean the place of someone who wasn't an elected official, not the place of a woman as you're suggesting.