“There are a number of people in our society . . . who do not fit neatly into either gender,” said Del. Sara N. Love (D-Montgomery), who co-sponsored the bill. “This is a recognition and a showing of respect of that.”

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Gov. Larry Hogan (R) has not taken a position on whether he will sign the bill, which passed both chambers of the ­Democratic-majority legislature by veto-proof majorities. Some GOP lawmakers angered LGBT advocates by objecting to the legislation, saying the state was trying to invent a new gender.

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The House approved the bill 89 to 49, largely along party lines. The Senate passed it 32-14.

Del. Haven N. Shoemaker Jr. (R-Carroll) said on the floor of the House of Delegates on Wednesday that the bill goes against religion and science.

“I checked my copy of the good book, and I saw where God created man, and God created a woman,” Shoemaker said. “I didn’t find anywhere where he created an X.”

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Roughly a third of transgender people across the country identify as “non-binary,” according to a 2015 survey by the National Center for Transgender Equality, which supports creating gender-neutral driver’s licenses.

A March 5 poll by Gonzales Research and Media Services found that 51 percent of Maryland residents did not favor giving drivers the option to identify as “unspecified” on their licenses, while 37 percent supported it and 12 percent did not answer the question.

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Also on Wednesday, the House voted 95 to 45 to reverse Hogan’s executive order that public schools start after Labor Day and end by June 15. The legislation, which passed in a different form in the Senate, returns control of the school calendar to local education boards.

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Extending summer break until Labor Day has support from most residents, polls show, but educators have criticized Hogan’s order as a power grab that keeps local school officials from arranging the schedule they believe would work best.

State lawmakers, anticipating that the governor’s supporters would petition the law to the 2020 ballot, took the unusual step of dictating how the bill would be described to voters if it were put to a public vote.

In a statement Wednesday evening, Hogan called the House action “politics at its worst” and a “thinly veiled attempt to manipulate the will of our citizens.”

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House Minority Leader Nicholaus R. Kipke (R-Anne Arundel), who opposed the bill, said the goal of the executive order is to give children the chance to “let summer be summer.” He said many Democratic lawmakers supported legislation to start school after Labor Day in the past but voiced opposition after Hogan signed the executive order.

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“What has changed?” Kipke asked. “Why is this necessary?”

Del. Anne R. Kaiser (D-Montgomery) said that for many poor children, “letting summer be summer is a longer summer slide and less access to food.” She said many parents have complained of higher child care costs and an inability to find summer camps.

The House also gave preliminary approval to the state’s $46.7 billion budget, trimming some of Hogan’s signature programs but largely advancing what he proposed.

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The spending plan — which will be up for final approval in the House this week before moving to the Senate — has no tax or fee increases for residents. The House added $325 million for public school education and a raise for state workers who did not negotiate one with the administration but reduced money for some of Hogan’s tax credits and programs to boost charter and private schools.

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In the Senate, lawmakers advanced bills that would legalize cannabis-infused edibles such as brownies for medical marijuana patients and prohibit minors from using tanning salons. The chamber also preliminarily approved a bill to allow an “enhanced penalty” when a person kills a woman knowing she is pregnant.

Under current law, young people can use tanning salons only if they have signed permission from their parents. Sen. Pamela G. ­Beidle (D-Anne Arundel) said lawmakers were told that some young people were forging the forms.

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Sen. Justin D. Ready (R-Carroll) said he thought the bill went “a step too far,” arguing that parents should bear the responsibility of deciding whether their teenagers go to tanning salons.

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Beidle said the legislation, which has stalled in previous years, is an attempt to “protect our children when their skin is most vulnerable.”