Idaho passed federally mandated child support rules on Monday, overcoming the objections of lawmakers who had rejected the bill in April over concerns that it would force American courts to comply with the laws of Muslim countries.

In a special session of the legislature, lawmakers approved the new child support rules, undoing a rejection that had jeopardized US involvement in an international treaty and threatened to collapse the state’s payment system. Rejecting the bill could have cost the state about $46m in federal funds.

In April, the bill was rejected by one vote on the final day of the legislative session, by state representatives who feared that the international treaty – which formalizes rules between nations for child support payments across borders – would subject Idaho to foreign laws, in particular those with underpinnings in Islam.

At the time, Republican representative Sheryl Nuxoll said that some countries listed in the treaty “have recognized sharia courts as quasi-courts”. Representative Lynn Luker downplayed the concerns voiced by Nuxoll and others in Idaho, saying that the bill was tabled because it and the treaty had “serious risks and flaws”.

Luker and three other former opponents of the bill voted in favor of it on Monday, after it had been amended to say that the state could not enforce any orders incompatible with Idaho law. Governor CL “Butch” Otter has said he will sign the bill into law.

By rejecting the bill, Idaho had threatened US participation in an international treaty that aims to streamline child support payments from parents who live abroad. Signatories to the treaty, which was mediated by the Hague Conference on Private International Law, agree to enforce child support judgments across borders. The EU and 32 nations have agreed to the treaty.

Colleen Delaney Eubanks, executive director of the National Child Support Enforcement Association, said that concerns over state sovereignty were baseless, and compared the new rules to the way that Idaho collects child support payments from Texas or any other US state.

“It’s making sure that all the countries that sign on to it are playing by the same general rules,” she said. “This is actually just modifying regulations that have been passed and implemented by states across the board.”

Under previous rules, states had to negotiate with countries directly. Twenty-eight states have passed compliance bills so far, according to the Department of Health and Human Services; Idaho was the only state to have resisted the treaty.

“How parentage and the orders are established are consistent across the board,” Eubanks said. “No state is required to sign on to anything that contradicts US law, and in no instance is somebody subject to another country’s law.”

Richard Armstrong, director of the Idaho department of health and welfare, testified to lawmakers that the treaty would let Idaho collect child support payments from parents abroad while protecting the state’s autonomy. Representative Heather Scott remained unconvinced, saying: “We are throwing away our state sovereignty and due process for efficiency.”

Armstrong and Eubanks stressed the costs Idaho would have incurred by rejecting the bill. “It would have pretty much dismantled Idaho’s child support program,” Eubanks said, noting that millions of federal dollars support programs such as Head Start and inter-state services.

Had it rejected the bill Idaho would have lost access to federal tools and databases, as well as $46m in federal funding. “It would’ve been a really dire thing for very vulnerable citizens of Idaho,” Eubanks said.

In committee, Democratic representative John Rusche asked his colleagues to set aside their “imaginary fears” of a threat to state sovereignty, but opponents of the bill said they felt the financial concerns tied up in the measure amounted to bullying and extortion by the federal government. One citizen quoted her Bible to the lawmakers, telling them: “Fire shall devour the houses of bribes.”

Some Republicans said they hoped Idaho would not rue the vote. Representative Mike Moyle told the Associated Press: “I pray that they’re right. I hope history proves they’re right because once you do this, you can’t undo this.”

The lawmakers who passed the bill celebrated its approval. “I think we did a really successful job,” Democratic senator Michelle Stennett told local KTVB news. “In the end we have to make sure our children are fed.” Her Republican colleague Brent Hill added that the lawmakers had addressed the issues on “a logical basis” and “a lot of fears went away”.