Updated: 4 p.m. CDT

BATON ROUGE, La. — Louisiana Gov. Bobby Jindal’s executive order that aims to give special protections to people who oppose same-sex marriage is unconstitutional and should be thrown out, gay rights advocates argue in a lawsuit filed Tuesday.

The American Civil Liberties Union Foundation of Louisiana, the Forum for Equality Foundation and six New Orleans residents lodged their challenge of the governor’s May 19 order in state court in Baton Rouge.

“Gov. Jindal has violated the Louisiana Constitution by setting up special protections for those who share his belief system. In our country no one is above the law, including the Governor,” Marjorie Esman, executive director of the ACLU of Louisiana, said in a written statement.

The lawsuit comes days after the U.S. Supreme Court effectively struck down bans on same-sex marriage in Louisiana and several other states. Louisiana parish clerks of court began issuing marriage licenses to same-sex couples Monday.

Jindal, who is courting evangelical voters in his campaign for the GOP presidential nomination, framed the executive order as a protection of “religious liberty” for Christians who oppose same-sex marriage and called the lawsuit an “attack” on civil liberties.

The “Marriage and Conscience” order prohibits state agencies under Jindal’s control from denying licenses, benefits, contracts or tax deductions in response to actions taken because of someone’s “religious belief that marriage is or should be recognized as the union of one man and one woman.”

The Republican governor issued the order after lawmakers refused to write similar provisions into Louisiana law.

The lawsuit claims Jindal tried to bypass the Legislature and make new law on his own, exceeding his constitutional authority and violating the separation of powers between the executive and legislative branches.

Jindal’s top lawyer referenced the order in a legal memo as licenses began being issued, saying officials who object to same-sex marriage on religious grounds don’t have to officiate at such weddings or approve the licenses.

However, the lawsuit says, “The governor is not authorized to create substantive law or create substantive benefits by means of an executive order.”

Jindal described the legal challenge as a “left wing lawsuit.”

“Religious liberty is fundamental to our freedom as Americans, and I will not back down from defending it,” he said in a statement.

But critics describe the order – just like the rejected legislation by Rep. Mike Johnson, R-Bossier City – as sanctioning discrimination against same-sex couples.

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Businesses opposed the bill, much like they did for similar proposals in Indiana, Arkansas and other states. Tourism leaders said it could heavily damage one of Louisiana’s most important industries. Critics in the legislature called Johnson’s bill an unnecessary distraction from important work of balancing next year’s budget and stabilizing the state’s finances.

When Jindal issued his executive order in May, some lawyers suggested it had no practical effect and was unenforceable because of limits on Jindal’s power through executive order. Jindal’s office dismissed the criticism.

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