Top Republicans in Texas have weighed in on two parents’ battle over their seven-year-old child’s gender identity, after the case was shared widely on social media and conservative news sites.

Anne Georgulas and Jeffrey Younger, from the Dallas area, have been embroiled in a legal dispute over their divorce and the care of their children since 2015.

Georgulas says the couple’s seven-year-old who was born a boy now identifies as a girl and prefers to be called by a female name.

Younger, who says the child acts like a boy around him, asked to be the sole decision-maker and launched a website in which he pleads for help to “save” his child.

The father finds comfort in public controversy and attention surrounded by his use of unfounded facts Judge Kim Cooks

Inaccurate and misleading stories have circulated in blogs, Facebook posts, YouTube videos and petitions. The Associated Press is not naming the seven-year-old to protect the child’s privacy.

Governor Greg Abbott tweeted this week that the attorney general’s office and Texas department of family and protective services (FPS) were looking into “the matter”.

The state attorney general, Ken Paxton, said he was asking FPS to investigate the mother for possible child abuse, citing “public reports” in a letter that alleged she was “forcing” the child to transition to a girl.

However, a judge said in a Thursday hearing in Dallas that the court noted no abuse, neglect or family violence in the case. Judge Kim Cooks ruled that the parents would make joint decisions about the child.

Cooks scolded the father, who she noted was unemployed, for seeking publicity and raising money on his website. But she also pointed out how the mother testified that her encouragement of the child being transgender may have been excessive.

“The father finds comfort in public controversy and attention surrounded by his use of unfounded facts and is thus motivated by financial gain,” Cooks said, adding that the gain came “at the cost of the protection and privacy of his children”.

Much of the public reaction to the case has focused on the narrative laid out on the father’s website, which features a headline saying he is fighting “chemical castration and sex-change of his son”.

A post of a woman holding a baby shared widely on Facebook targets the mother, saying she “always wanted a girl”.

Cooks said no Texas court or judge has ordered “the chemical castration, puberty blockers, hormone blockers or any transgender reassignment surgery on this child to become a female”.

Attorneys for Georgulas, who is a pediatrician, said before the hearing she was “being viciously attacked and threatened by complete strangers based on false and untrue statements”. Cooks said she limited spectators to only the media at the hearing because of safety concerns.

Earlier this month, Georgulas filed a proposed parenting plan that said the child is not yet at an age where treatment with hormonal suppression, puberty blockers or gender reassignment surgery is considered. And she asked the court to not allow any such treatment without the consent of both parents.

Cooks said the court found that both parents love their children, and noted the seven-year-old appears comfortable as a male or female.

Younger told the AP the child identifies as a boy when at his house. Asked after the hearing if he was happy, he only smiled and nodded.