“There’s really no difference, which is actually quite remarkable when you think about the additional layer of stigma these children are growing up with,” she said.

Critics of same-sex parenting have frequently pointed to a 2012 study by a University of Texas sociologist that suggests children of gay and lesbian parents are significantly different from children raised by heterosexual couples. That study has been roundly criticized by others in academia.

Judge Nance’s decision to recuse himself comes less than two years after Kim Davis, a county clerk in Kentucky, defied federal court orders to issue same-sex marriage licenses because it went against her Christian beliefs. She was jailed for her refusal and became a symbol of the resistance to same-sex marriage.

The Family Foundation, a Lexington-based group that says it seeks to “strengthen Kentucky families,” offered praise for Judge Nance’s decision, saying, “Judges have a right of conscience like everyone else.”

“If we are going to let liberal judges write their personal biases and prejudices into law, as we have done on issues of marriage and sexuality, then, in the interest of fairness, we are going to have to allow judges with different views to at least recuse themselves from such cases,” Martin Cothran, a spokesman for the group, said in a statement.

Other judges have faced consequences for similar stances on L.G.B.T. issues. A judge in Wyoming was censured in March for refusing to perform same-sex marriage ceremonies, and an Alabama judge was suspended in September for ordering probate judges to defy federal orders to issue marriage licenses.

Some critics called for Judge Nance to resign or face ethics charges after Thursday’s order. Chris Hartman, director of the Fairness Campaign, an L.G.B.T. advocacy group, said the order displayed “clear discrimination.”