* On mobile disclaimer * 1964 was a year preceded by progressive presidents (Roosevelt, Truman, Eisenhower, Kennedy) with their General Election opponents also being quite progressive (Nixon, Dewey, Stevenson). That's thirty years of economic policy that, very broadly speaking, favored policy change accompanied by federal involvement. So, the conservative and reactionary wings of Republican Party hadn't fielded a party nominee for the presidency in 30 years. This is partially because the last two Presidents in recent history that could claim economic conservatism were blamed (particularly Hoover) for the Great Depression.

The honeymoon in the wake of WW2 was long gone and even the Korean War had 'finished'. Relations with the USSR had long been dicey and we were about a year and a half removed from the Cuban Missile Crisis. Foreign policy was on everyone's mind and it looked like what we had been doing maybe wasn't working so well.

Tensions were rising as protests about reestablishing black civil rights were at a fever pitch and the last three Democratic Presidents made overtures of support. Truman integrated the armed forces, Kennedy was endorsed publicly by MLK Jr, but most notably Johnson would sign the Civil Rights Act into law a week before the Republican convention. Within the reactionary and segregationist wing of the Republican Party, George Wallace made his "Segregation now, Segregation forever" speech in 1963. He would later go on to run the last third party candidacy to capture electoral votes in 1968.

All this to say that Barry Goldwater captured the voices of many people who felt disenfranchised by the options that had presented themselves in the recent past, and were attracted by his aggressive alternative in foreign policy and military affairs. Most crucially he opposed the Civil Rights Act, largely under liberatarian objections against Federal involvement in business and personal life. This objection gave segregationists a candidate to coalesce under in the 1964 primary.

I'd say that Goldwater was primarily the beneficiary of reactionary, conservative, and segregationist voters wielding organized political power in the wake of the New Deal coalition beginning to dissolve under the weight of civil rights policy. This power can be seen more blatantly in George Wallace's bid in 1968 under the segregationist American Freedom Party.

None of this is to say the Goldwater was a wildly popular candidate - he grabbed just 22% of New Hampshire voters, and only won 7/16 Republican primaries. It's safe to say that his rhetoric and segregationist-friendly policy was relatively unpopular even inside his own party, but the thing going for Goldwater is that progressive Republicans voted and supported 5 different opposing candidates (Nelson Rockefeller, most notably) and that weakened their ability to counter Goldwater's nomination.

I hope that at least adds some context to consider. I'll stamp some sources on if you'd like (when not on mobile).