The best part of the English language, American-style, is that it is fluid. In my life I have watched the words "pimp" and "hack" go from pejorative to adulatory. The masculine baggage associated with any given word is generally one use case from vanishing forever.I'm having trouble with the word presidential.
So true about "hack" to the point that winning a hackathon is brag-worthy. Language is absolutely fluid. I'd love to see the meaning of "presidential" to be firmly in the realm that steve suggests below (thoughtful and having integrity) along with the meanings that b_b embraces. The Canadian Oxford Dictionary doesn't bother to suggest any definitions -- merely that it is the adjective form of "president." Being presidential is not a big deal in Canada and we never talk about being prime ministerial. Like language in general, people will assume the meanings of words --- until their assumptions lead to misunderstandings. I'm grateful for people who frequently say, "What do you mean?" before assuming they understand.
It's very much an American word. The world has had dozens of female prime ministers so female leadership isn't particularly novel. However, American democracy, being basically a Mennonite political system, remains chauvinist. I am eager for this to change.