WASHINGTON — On Tuesday night, South Dakota’s Republican governor, Dennis Daugaard, became the first governor to veto a bill that would restrict transgender students’ access to public school bathrooms and locker rooms.

Daugaard’s argument didn’t necessarily weigh in on the morality of requiring students to use the bathroom of their biological gender.

Rather, he vetoed the bill because he said that state government doesn’t need to be stepping into what is really a local school issue.

It’s a conservative reason to support – or at least not oppose – a cause that is mostly championed by liberals. Daugaard’s conservative framing of so-called “bathroom bills” may be just what lesbian, gay, bisexual and transgender advocates need to swing what’s become a heated cultural battle on transgender rights in their favor.

Here’s what Daugaard said when issuing his veto, which he had until midnight Tuesday to do:

“Local school districts can, and have, made necessary restroom and locker room accommodations that serve the best interests of all students, regardless of biological sex or gender identity. This bill seeks to impose statewide standards on ‘every restroom, locker room, and shower room located in a public elementary or secondary school.’ ”

In other words: Why get the state involved when local school districts can figure this out for themselves? Daugaard’s reasoning gets to the heart of conservatism, which is to get government out of the way of the people.

Plus, if it became law, South Dakota would stand in direct conflict with federal policy on bathrooms and gender, inviting litigation and threatening the loss of millions of federal dollars. Daugaard also noted those consequences in his veto message to lawmakers.

LGBT advocates like Human Rights Campaign’s Kate Oakley would agree with Daugaard’s basic premise for rejecting the bill. There’s no need for state legislatures to require schools to handle transgender students a certain way when the issue can be handled privately between the student, the student’s parents and school administrators, she said.

“If this is done right, it should be that a trans student is able to use a restroom or locker room and other students might not even know they’re transgender,” she told The Fix in February, as the South Dakota bill was being debated in the Republican legislature.

Supporters of the bill say it would have protected the privacy of students, both trans and not, from uncomfortable and even inappropriate situations.

“It’s very simple: Boys in the boys’ shower. Girls in the girls’ shower. Accommodation for students who are transgender,” state Rep. Fred Deutsch, a Republican, told The Washington Post’s Emma Brown on Tuesday.

Daugaard’s veto was a big break for LGBT advocates who sorely needed it. South Dakota was one of about a dozen states considering so-called “bathroom bills,” or bills that require a student to use a bathroom and locker room corresponding to his or her biological sex rather than a chosen gender.

More broadly, LGBT advocates are playing a frantic game of Whac-A-Mole in state legislatures across the nation, which are debating bills that advocates fear would roll back gay rights they won recently at the federal level.

But after Tuesday, LGBT advocates can add a conservative argument for their cause to their arsenal, courtesy of South Dakota Gov. Dennis Daugaard.

— The Washington Post News Service with Bloomberg News