A little over a week ago, President Donald Trump announced on Twitter that the US military would no longer let transgender people serve in the military, reversing the policy established by former President Barrack Obama.
The poll also found respondents supportive of LGBT people in other ways.
Trump's latest Quinnipiac approval rating is worse than the 55-to-40 percent disapproval mark recorded in its last survey in late June.
60 - 32 percent of Republicans oppose transgender service, but every other party, gender, education, age or racial group supports it by margins of 22 percentage points or higher.
A Gallup poll from August 1 shows similar levels of negative sentiment.
"It's hard to pick what is the most alarming number in the troubling trail of new lows for President Donald Trump", Tim Malloy, assistant director of the Quinnipiac Poll, said.
A majority of Republicans, 60 percent, oppose allowing transgender people to serve in the military.More news: The PS4 Has Now Shipped 63.3 Million Units, Sony's Revenue Trending Upward
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Among all Americans, 68 percent think transgender people should be allowed to serve in the military, compared to 27 percent who think the opposite. The pollster said that Americans by a 54-to-26 percent margin said they are embarrassed rather than proud to have Trump as president.
The May 17 New York City poll found Mayor de Blasio's approval rating soars; he tops little-known challengers 3-1.
64 - 25 percent of voters disapprove of Republican ideas to replace the Affordable Care Act.
The key vote in the U.S. Senate that rejected the health care repeal bill came between midnight and dawn last Friday.
It found that 62% disapprove of Donald Trump, well ahead of the 38% who approve of his performance, giving him a net approval rating of -24%.
Frequently cited by journalists, public officials and researchers, the independent Quinnipiac University Poll regularly surveys residents in Colorado, Connecticut, Florida, Iowa, New Jersey, New York, Ohio, Pennsylvania, Virginia and nationwide about political races, state and national elections, and issues of public concern, such as schools, taxes, transportation, municipal services and the environment. And (standard poll-story disclaimer) this is only one poll.