From 2016, married men/unmarried women trended left. Unmarried men/married women trended right. Why?

[Skill and Chance]

Recent history in exit polls for married women:

2012: R+7 (NPV D+3.9)
2014: R+10 (NPV R+5.7)
2016: D+2 (NPV D+2.1)
2018: D+10  (NPV D+8.6)
2020: R+4 (NPV D+4.5)
2022: R+14 (NPV R+2.9)

This really looks like a one-time swing to Hillary Clinton as the 1st female nominee and then a quick reversion to their historical R-leaning voting patterns.  Note that they stuck around for Dems one more time in 2018, so MeToo backlash doesn't fit as an explanation for why they are back to voting R now.  If it does come down to a specific issue, a COVID restrictions/"woke" school curriculum backlash seems more plausible with this timing.

[Skill and Chance]

With women, I think it's just that liberal women seem to be less likely to get married, at least formally married than more conservative women, and the age divide has only grown more extreme and hence the partisan divide.

Every year, we do inch closer to a world where getting married = culturally conservative by default. However, we aren't particularly close to that point.  A supermajority still get married at some point in their lives.

[Skill and Chance]

Recent history in exit polls for married women:

2012: R+7 (NPV D+3.9)
2014: R+10 (NPV R+5.7)
2016: D+2 (NPV D+2.1)
2018: D+10  (NPV D+8.6)
2020: R+4 (NPV D+4.5)
2022: R+14 (NPV R+2.9)

This really looks like a one-time swing to Hillary Clinton as the 1st female nominee and then a quick reversion to their historical R-leaning voting patterns.  Note that they stuck around for Dems one more time in 2018, so MeToo backlash doesn't fit as an explanation for why they are back to voting R now.  If it does come down to a specific issue, a COVID restrictions/"woke" school curriculum backlash seems more plausible with this timing.

Yeah QAnon and lockdowns (combined with 45's stimulus) explain a good chunk of the 2018-2020 swing. Wouldn't have expected school curriculum backlash to be a significant factor unless I'm underestimating how much more married >40 women care about this stuff (even if they don't have K-12 age children!) than their unmarried >40 counterparts.

The 2020-2020 R+10 shift among married women could be largely fueled by backlash over school curriculum issues ("CRT", LGBTQ+ inclusion), and possible COVID vaccine mandates for schools.

Why didn't married men shift as well then? Is the GOP just really close to their ceiling with married men at the moment?

Probably.  In 2020, white men moved meaningfully left from 2016 and elected Biden while nearly every other demographic moved right.