Gov. Charlie Baker of Massachusetts, who enjoys wide popularity in his state, has worked closely with the Democrat-controlled legislature to increase the minimum wage and create a paid family and medical leave program. Gov. Phil Scott of Vermont has defended the Affordable Care Act, and has supported free trade in a state that does a lot of business with Canada.

While criticizing the president can be a political death sentence for many Republicans, it is more of a life raft for governors in these states. Mr. Hogan was an early rejecter of Mr. Trump, and Mr. Scott and Mr. Baker have openly criticized the president’s policies. All are rated safe or nearly so by political strategists who study governors’ races.

“Three of the five most popular governors are Republicans in blue states,” said Jennifer E. Duffy, senior editor for The Cook Political Report, an independent newsletter in Washington. “These are governors who have largely proven that they are more in sync with the voters in those states, and what they want and need, than what their party wants from them.”

These Republicans might be expected to draw strong challenges from more conservative candidates, but a popular governor is not a great target, and Republican voters have largely overlooked any left-leaning proclivities their governors exhibit.

“I was a little disappointed when he pulled troops from the border,” said Krista Hudson, 50, an admirer of Mr. Trump who lives in this rural stronghold of Mr. Hogan’s. “But I still support him. This is a Democratic state, and we have always felt ignored and neglected, and we just see him a lot down here.”

Nor have many Democrats stepped up to take on these popular governors. “We should not neglect the fact that the Democrats running are pretty weak,” said Dan Payne, a Democratic strategist in Massachusetts, where a primary next month will determine who will take on Mr. Baker.