I imagine it swung hard R in 2016, given Trump's early attempts to distance himself from Southern Evangelical party orthodoxy (though its disingenuity was clear) and, at the risk of going full "Gamergate is responsible for the entire contemporary political landscape", how much of contemporary online far-right thought emerged from the whole greater r/atheism scene. I highly doubt that it outright went R, though.
As someone who was rather active in those circles during their heyday, there certainly was a response of "oh f---- off" within the community to being told Cortana set unrealistic body standards or GTA appealed to the male fantasy. That said, that well of misogyny had long existed; It very much was a thing of "I'm not letting the f---s who made Wincest and furries popular ruin my video games, let alone have an idea of running general society."
The real culprit if any imo was the long-running strands of Islamophobia in the New Atheist Movement. Numerous figures such as Dawkins, Maher, Sam Harris, The Amazing Atheist, Sargon, and so forth all cut their teeth on criticizing the human rights abuses towards women and non-believers.
Enter the Don. Trump's image as an amoral reality TV star might've actually helped him in this regard. Instead of railing against homosexuality as an abomination, he was promising to defend the LGBT community in light of the Pulse nightclub shooting. Instead of being the candidate whom would strip away the right to choose (though he made sure to emphasize the anti-abortion plank and importance of appointing justices to the right audiences), the alt-right race-baited by playing up fears of Arab men assaulting white women. Throw in the organic full-time operation /pol/ was running plus Bannon's microtargeting and it is very clear there was a concerted effort to target this group.
Most exit polls still had the atheist/unaffiliated vote breaking ~2/1 for HRC with a relatively high 3rd-party share, relatively in line with the D-R split among the group in public surveys to this day. It does not appear to be much of a coincidence that the demographic profile (young, white, male, likely residing in the Northeast if not the West Coast) also had heavy enthusiasm for Bernie. Did this crucial portion swing to Trump, or rather did the aforementioned above lead to a critical portion either voting 3rd-party or simply stay home?
