The district’s spokesman, David Stephenson, said in an email that “the school took appropriate action that day based upon their investigation,” but referred questions on the substitute teacher to Kelly Services, the staffing company used by the district. The district did not identify the teacher.

Kelly Services said in a statement on Sunday that the substitute teacher was no longer employed by the company.

“We are concerned about any reports of inappropriate conduct and take these matters very seriously,” the statement said. “We conducted an investigation and made the decision to end the employee’s relationship with Kelly Services.”

The company did not respond to questions about how long the substitute teacher had been placed in the school district or the vetting process it used for school instructors.

Mr. van Amstel said he was proud of how swiftly and decisively the school had handled the situation, but was troubled about the vetting of the teacher and about how she had tried to impose her personal beliefs on a group of children.

Mr. van Amstel, an Amsterdam-born choreographer, former dance champion and creator of the dance fitness program LaBlast, said his neighbors in Utah had rallied around his family. He said some online commenters had jumped to unfair conclusions about what he described as a politically and socially conservative state.

“It doesn’t mean that all of Utah is now bad,” he said. “This is one person.”

The episode came just a few weeks after the Trump administration proposed a rule change that would roll back Obama-era discrimination protections that were based on sexual orientation and gender identity. Advocates for lesbian, gay, bisexual and transgender families have said that the reversal could allow foster care and adoption agencies to deny their services to L.G.B.T.Q. families on faith-based grounds.