The most likely actual outcome is the splintering of the Dems. The Democratic Party right now is a fusion of progressive/leftists (mostly young), centrist neoliberal types who would be republicans if the Republican Party stood for anything these days, and minorities who are sometimes pretty conservative but are driven away from the Republican Party by the base's white nationalism. The Republican Party has succeeded so well at driving away natural allies that they're likely to be absolutely crushed at the national level this year and for the foreseeable future, and only an intense gerrymander will save their House majority. Even that is likely to end in 2020 when the next redistricting happens because presidential year elections favor Democrats due to increased turnout.
This is not sustainable. Long term what's likely to happen is the complete disintegration of the current Republican coalition, with the white nationalists and hardcore revanchists disenfranchised. The next Trump-like candidate is going to be carpet bombed out of existence with every dirty trick the Party can come up with to prevent a recurrence of this outcome. Trump's base will either quietly fall in line with the new Republican consensus, split off into no-hoped third parties, or die off (a lot of them are old and the Baby Boomers are starting to die in real numbers).
This will leave the neocon hawks, the fiscal conservatives, the Grover Norquist types. They have natural allies in the right wing of the Democratic Party. Think Ben Nelson and the like. In my opinion the most likely vehicle for this is more conservative voters leaving the Democratic Party to vote for moderate Rs, but the Republican brand is in the toilet right now so it's possible that the reverse happens and for a while, the Democratic Primary becomes the real race in a number of swing states the way it is now in places like Massachusetts. This comes to a head the next time the Dems have to nominate a president, leaving a fissure that splits them into two parties while the old Republicans fade to rump status except maybe in the Old South. The factor that could delay this is that as long as the Republican Party keeps nominating insane old authoritarians, the people who WOULD be leaving the Democrats will be scared into staying.
Oh, and as far as the men/women thing: if it was as simple as "republicans for men, democrats for women" democrats would win every race from now until the end of time. There are more women than men in the electorate and that trend is accelerating, not reversing. There are plenty of women who vote for republican candidates, though not as many this year, and plenty of men who would rather be democrats. There are more than two categories though and if you're a black, Latino, gay, or Muslim man, you are overwhelmingly likely to support Dems because of the Republican base's open hostility. That sort of works in reverse, with white women being a traditional Republican constituency, but Clinton is on track to win them for the first time in a WHILE because of Trump.