So how does The Big Sort affect marriage?
Bill Bishop, in the book of that name, is dealing with counties as his main unit of analysis, so it is hard to tell directly how marriage is affected by his finding. As a default, he takes couples with children as the unit that he assumes chooses neighborhoods. This is not a bias so much as a simplifying assumption. Since most people do marry and have kids, this is not a bad assumption. It does, though, obscure some important nuances.
In particular, many strongly Democratic neighborhoods are full of single people, while the Republican exurbs are very family-oriented. Other researchers have found that the famous "gender gap" in voting is mostly a marriage gap. Married people are more likely to vote Republican; singles, Democratic. Since there are more single women than single men, this looks like a gender gap.
Indeed, most marrieds have a stage in life when they are living single. At that stage, in the college-going class, anyway, they are more likely to live in an urban area where they worry less about protecting and educating little ones. At a later stage in life, with kids to worry about, they move someplace with more room and less danger. If they changed their voting habits with that move out, that would be a big part of the explanation of The Big Sort.
Which is a good start for the next research project.