Vermont isn't just more Democratic than it's ever been, it's more liberal. There's a sizable "Take Back Vermont" movement, and if you talk to older Vermonters (keep in mind even in the biggest Democratic landslides, you have about 40% supporting the Republican), you'll notice they're not as pleased with the trend of the '70s, '80s and '90s, which saw liberal New Yorkers (Howard Dean, anyone?) and folks escaping Taxachusetts and Connecticut to go to the scenic and rather "undisturbed" Vermont. There have also been quite a few VT Republicans and former Republicans who have been turned off by social conservatives gaining more influence in the GOP. Combine those two things and you get a Democratic VT.
So, you'd need BOTH of these to happen to get VT back in the Republican column:
1) The GOP to become significantly more moderate on cultural and social issues.
2) An influx of more conservative voters and/or more liberal voters moving away.
Here's what I don't get...if it's really demographic changes during that time that caused VT to go Dem, how did Johnson not only win it in '64, but win it by a bigger margin than his national one?
I think demographic changes played some role, but something else happened.
Something else did happen, and that was my second point. But people can't make statements like "VT went solid Dem in '64" or "MS went solid GOP in '72" with any real point attached because so did every other state...
But it's of interest whether a state goes for the party by a bigger or smaller margin than the nation as a whole did. Vermont had never voted for a Democrat, but voted for LBJ over Goldwater by a 32-point margin as opposed to the national 23-point margin. If LBJ'S Vermont margin had been the same or less than his national margin, then I agree it wouldn't really be of interest. Something about Goldwater really turned off New England voters a generation before New England would actually be thought of as Democratic region.
Civil Rights issue, duh. Goldwater's stance on the 1964 Civil Rights Act, even if he had an exceptional record before, kind of made him political poison to New Englanders. It didn't even help him with working class racists who preferred the Democratic Party normally because a) his economic record was also very right wing (New England blue collars were/probably still are some of the most unionized groups in American society), and b) they really didn't see the point of it as minorities in general knew to avoid "that part of town" anyway.
Really, the 1960's GOP chose some of the worst candidates to appeal to New Englanders. In 1960 they decided to nominate Nixon/Lodge. Nixon got his name from being a huge red baiter and an advocate of conservatism (I got to laugh at people who think he was the more liberal candidate in 1960, I mean come on) while the Lodge name wasn't exactly as grand as it used to be in Massachusetts (many ethnics would reflexively vote against anyone whose last name was "Lodge" and even many New England WASPs would vote for Kennedy because of his moderate pragmatic record and the prestige his record brought the region. Really, a no winner). Of course, Lodge was nominated largely for his foreign policy accolades more than anything as Nixon desperately needed a runningmate who could make him look good on international issues as well as carry some appeal with more moderate and liberal Republicans.
1964 was even worse, as Goldwater's extreme right wing views turned off most moderate and liberal New Englanders in droves. If they weren't outraged by his Civil Rights views they would certainly be outraged by his economic ones (hell, Alaska voted against him in landslide margins because he wouldn't even support disaster relief for the state after the 1964 Anchorage Earthquake). Really, here is where you got a generation of people in New England who were strongly opposed to Republicanism and I think I heard somewhere that Massachusetts is one of the only states in the union where people over 65 vote more Democratic than any other age group.
1968? Well, Nixon again with Agnew versus Hubert Humphrey and Edmund Muskie. This time it was more advantage Democrat than it was the GOP ticket being unappealing (though that did have some effect). Muskie was a well known and popular "moderate" governor of Maine who was on the forefront of the environmental reform movement. Humphrey was, in addition to being a champion of Civil Rights, one of the biggest cheerleaders of organized labor and one of the key advocates for the AFL-CIO. It also didn't help that Nixon made a point of bashing intellectual "elites" and had a hardon for Harvard. Thus again, the GOP chose candidates that did not appeal to moderate upper class whites who in the past voted for them largely on the Civil Rights issue and at the same time could not appeal to somewhat reactionary working class whites who were still pretty favorable to Democratic dominated unions.
In 1972, when the widely reviled by unions but still closet commie George McGovern was nominated by Democrats, that gave the GOP an opening with upper middle class folk and pro-union working class whites and united them against a made up strawman of radical intellectuals, closet homos, uppity non-whites taking their new freedoms for granted, and Harvard Alumni.
That's at least what I'm theorizing.