Describe a 1964 LBJ voter who voted Republican in every other Presidential election they voted in

[TransfemmeGoreVidal]

Probably not all that uncommon actually: a suburban or rural Republican who was terrified at Goldwater's idea of giving combat commanders the authority to use nuclear weapons. Probably also a considerable number of northern Republicans who were put off by Goldwater's opposition to the Civil Rights Act (though he opposed it for non-racist reasons).

People often try to rehabilitate him with that, but even if his own personal reasons weren't racist, why did he campaign so aggressively in the South then? Did he think they opposed the Civil Rights Act for non-racist reasons?

and also does it really matter what his intent was when they end result would have been continuing discrimination?

[Skill and Chance]

I knew someone who fit this.  He grew up in a historically Republican part of eastern Pennsylvania.  Primarily German descent and largely non-practicing Lutheran.  Did not attend college but practiced a skilled trade.  He became a reasonably successful businessman and leader of a Masonic Lodge.  Lifelong distrust of anything too culturally Southern.  He passed away just prior to the 2016 election.

[Gracile]

A decent number of Yankee Republicans in Western New York fit this description. Several counties in that region only voted for a Democrat during the 20th century and onward in '64 (Wayne, Allegany, Livingston, etc.).

[I Will Not Be Wrong]

Both Clinton County and Warren County in Ohio have voted Republican in every election since 1856 except for 1964, so probably somebody from one of those counties. Central Western Ohio has many historically Republican counties that nearly all voted for LBJ, except for Fulton and Union (others in that region that did vote for LBJ were Fayette, Madison, Logan, Greene, and Champaign).

Allegan County, Michigan would also apply here, if you excuse Teddy winning in 1912. There has to be several of these voters in that county. Antrim County, Michigan and Randolph County, Indiana would apply here too.

[Pericles]

A Vermonter who died any time before the 1990s.