Ken Paxton and a Texas Catholic archdiocese want foster and adoption agencies to be able to turn away LGBTQ people and still receive federal funds.
The Republican administration said last week adoption services could refuse to place childen with rainbow families.
The couple and their sons fled Russia, which does not allow same-sex couples to adopt.
The federal judge contends an adoption agency that won't serve LGBTQ parents doesn't really discriminate because it sends them elsewhere.
Andrei Vaganov and Yevgeny Yerofeyev say they also could be arrested for sexual abuse or even murder due to the government's homophobia.
This comedic docuseries shares a Bay Area queer couple's journey in the process of adopting from foster care.
The case represents a new application of the country's notorious "gay propaganda" law.