“There’s no question the presidential trail goes through places that congressional Republicans don’t always have to go,” said Ari Fleischer, the first White House press secretary for George W. Bush, the last Republican to win the party’s nomination largely because of strength in red-state primaries. Mr. Bush struggled in blue states, losing early primaries in New Hampshire and Michigan, but still secured the nomination.

The importance of blue-state Republicans makes it far less likely that the party will nominate a conservative firebrand or a favorite of the religious right, like Ted Cruz or Mike Huckabee, than one might guess from the unwavering conservatism of the red-state electorates that hold sway over elected Republicans in Washington. It also makes the primaries the party’s best chance to moderate its image in hopes of faring better in presidential elections, as the Democrats did in 1992 by nominating Bill Clinton, a Southern Democrat. The pre-eminence of red-state conservative Republicans in Washington has made it all but impossible for congressional Republicans to compromise, moderate or rebrand the party ahead of the 2016 elections.

It would be hard for the Republicans to nominate a true moderate who disagreed with the party’s conservative base on more than a few issues. Most blue-state Republicans are conservatives, but they are nonetheless very different from their red-state counterparts. Moderate Republican politicians, like Mr. McCain or Mr. Romney, have been forced to evolve into more conservative candidates on issues like immigration or climate change. Yet Mr. McCain and Mr. Romney would have struggled to win the nomination without the blue-state Republicans.

The tendency of a national primary electorate to moderate a party isn’t new. And it’s not limited to the Republicans. Mr. Clinton won just three of the first 15 contests in 1992, losing relatively liberal Maryland, Colorado and New Hampshire before sweeping eight Southern primaries on Super Tuesday. Hillary Clinton would have a huge advantage over a candidate who challenged her from the left. Such a candidate might win San Francisco, Boulder, Colo., or Vermont, but would struggle to win relatively conservative Democrats in Appalachia or the South.

According to an analysis of Pew Research and exit-poll data, blue-state Republicans tend to be more urban, more moderate, less religious and more affluent. A majority of red-state Republicans are evangelical Christians, believe society should discourage homosexuality, think politicians should do what it takes to undermine the Affordable Care Act and want politicians to stand up for their positions, even if that means little gets done in Washington. A majority of blue-state Republicans differ on every count.

In recent presidential primaries, blue-state Republican voters have overwhelmingly supported so-called establishment candidates. On Super Tuesday in 2008, Mr. McCain all but locked up the nomination by winning delegate-rich blue states like Illinois, New York, California and New Jersey. Yet outside of his home state, he lost nine of the 11 red-state contests on that night. Mr. Romney lost all but one red-state primary held before his principal opponent dropped out of the race, yet he won the nomination by sweeping the blue states. He won 45 percent of the vote in blue-state primaries, but just 30 percent in the states that voted for him in the general election.