Ask yourself a question: why can't a woman become a preacher, priest or pastor? All major US religions indoctrinate their followers from birth with the teachings that god does NOT permit women to exercise authority over men.
So if Christian and Catholic men and women believe in a core set of values and reasons for why women are not allowed to take leadership roles over men in the church, what makes anyone think they don't or won't apply that same logic to leadership at the political level, or ANY level?
Christians won't let a woman lead their church, but they somehow will be OK with electing a woman into a much higher role, one that can make decisions that affect all churches/the entire world? I don't see it.
In Christianity, the bible forbids women from exercising authority over men in the church - they are forbidden from any leadership role within the church. This begs the question: what makes you think Christians will vote to elect a woman to the highest level of leadership this country has, into a position where she can make decisions affecting not just one church, but every single church across the US?