Moderate Republicans cannot fathom what has happened to their party.

Once a happy band of no-nonsense, pro-business conservatives, cautious in everything from money to marriage — including their wary response to the onward march of 1960s liberal social values — they were prepared, within reason, to trim their policies to match the voters’ mood. After all, to achieve anything in government you first have to win elections.

But that was before the revival in fundamental conservatism that has turned the GOP from a pragmatic party to a collection of inward-looking ideological tribes. Republicans puzzled by the rise of dogma and division in their party can find answers in a new survey that explains how large the factions are and what they think. They will be surprised by the findings.

The GOP has long been considered a three-legged stool: big business, Southern evangelical Christians and anti-government Westerners. But, largely since the world financial panic of 2008-9, these three have been joined by two new aggressive, popular movements: the Tea Party and the libertarians.

To put the transformation of the GOP in context: the only postwar departure from steady, old-school Republican moderation was an experiment in conservative radicalism in 1964 when the government-hating Barry M. Goldwater became the party’s presidential champion.

The result was disaster: “Mr. Republican” was painted by his opponent President Lyndon B. Johnson as a trigger-happy rube who would trip nuclear war with the Russians.