A new survey shows one of the most competitive battles on the Massachusetts ballot this fall may be a question on whether to repeal the state’s antidiscrimination law on transgender rights.
Forty-nine percent of respondents said they would keep the law, while 37 percent said they would vote to repeal it and 13 percent said they were undecided, according to the poll from Suffolk University Political Research Center released on Thursday.
The 2016 law, signed by Governor Charlie Baker, bans discrimination against transgender individuals in public places, such as hotels, stores, and restaurants. Most controversially, it allows transgender individuals to use bathrooms that match their gender identity.
Some critics have suggested the ballot’s wording — which asks voters whether they want to keep the law — is confusing.
Yvette Ollada, of Keep MA Safe, which is campaigning for repeal, said that education is going to be key in winning over voters.
“There is a lot of misinformation about this,” Ollada said. “What we are saying is to repeal the law so that the Legislature can start over to make a law that provides accommodations for everyone and protects everyone.”
Matthew Wilder, a spokesman for Freedom for All Massachusetts, a coalition advocating to keep the law, said there’s much more at stake in the law’s repeal than bathrooms.
“This is an anti-discrimination law about hotels, and stores and being able to go to sports arenas,” said Wilder. “I think that when voters realize that, then more people will support it beyond the narrow focus of this poll.”
Also key to both sides: people understand what the ballot question is asking.
“We knew going in that those polled would have questions, and we did our best to clarify what we could, but no one will be answering questions in the ballot booth,” said David Paleologos, the director of Suffolk University Political Research Center.
On other ballot measures, the survey found voters were more decisive: by a 2-to-1 margin, they said that they wanted to increase income taxes on in-state residents earning at least $1 million annually and, separately, they wanted to gradually raise the minimum wage to $15 an hour.
The Massachusetts Supreme Judicial Court is expected to rule soon on whether the so-called millionaire tax is constitutional. If not, the question will not be on the fall ballot.
Suffolk University conducted the poll from June 8 to 12 on landlines and cellphone numbers, surveying 500 Massachusetts residents who said they were “very likely” or “somewhat likely” to vote this fall. The poll’s margin of error is 4.4 percent.
The two top statewide races on the ballot this year — for governor and US Senate — continue to be lopsided in favor of the incumbents, the survey found.
Baker, a Republican, has commanding 30-point leads over both Democrats, Jay Gonzalez and Bob Massie, who will square off in the Sept. 4 primary. US Senator Elizabeth Warren leads all three of her potential GOP challengers by about the same margin.
However, the survey also showed that Warren and Baker pulled support from vastly different swaths of state voters.
Baker’s support is roughly even across the partisan spectrum, whereas Warren’s support, per the survey, is much more polarized.
Among those approving of Baker’s job performance as governor in the poll: 61 percent of Republicans, 63 percent of independent or unenrolled, and a majority of Democrats: 54 percent.
Warren, meanwhile, had 89 percent of Democrats approving of her performance as a senator, while only 42 percent of independents approved and just 7 percent of Republicans did.
“The poll reflects that while they get to the same place, Baker and Warren are very different people with very different jobs,” Paleologos said.
One outside factor that weighs on both statewide officials is President Trump, who is still deeply unpopular in the state. Sixty-two percent of likely Massachusetts voters disapproved of Trump, while 30 approved and 7 percent were undecided in the survey.
The poll also showed that voters largely view Baker, who has been critical of Trump, as someone who is not supportive of the president. When asked, 59 percent said that Baker was generally “anti-Trump” while 14 percent said he was “pro-Trump.”
During the 2016 presidential election, Baker publicly questioned whether Trump had “the temperament to serve as president.” Since Trump’s election, Baker’s involvement with the White House has been mostly limited to a commission on the opioid crisis.
Baker’s primary opponent, anti-gay pastor Scott Lively of Springfield, has called his candidacy “100 percent pro-Trump.” That message resonates with Republican Barbara Atwood, 68, a telecom-munications engineer from Dorchester.
“I am a Trump supporter, and [Baker] didn’t vote for Trump,” said Atwood, who added she plans to write in Lively’s name in November if he’s not the nominee.
At the same time, Baker’s distance from Trump increases his appeal with Democrats like Joan Ayers, a retired hospice chaplain from Fall River who participated in the survey.
Ayers said she views Baker as a different Republican than Trump because the governor “is just a polite guy, and that counts for something.” She said she would be open to voting for either of Baker’s Democratic challengers, but she hasn’t heard anything about them.
Twenty-five percent of voters surveyed said they are undecided in the governor’s race.
James Pindell can be reached at firstname.lastname@example.org. Follow him on Twitter @jamespindell or subscribe to his Ground Game newsletter on politics: http://pages.email. bostonglobe.com/GroundGameSignUp