Gay and lesbian rights organisation Stonewall took a swipe at the Christian Institute charity after the House of Lords voted to repeal Section 28 of the Local Government Act last week.
Stonewall chief executive Ben Summerskill hailed the ruling as "a triumph for 21st century tolerance over 19th century prejudice".
He said: "We regret that organisations such as the Christian Institute found it necessary to resort to distortion and scaremongering in their attempts to frustrate this long overdue change in the law."
The institute led calls for the retention of Section 28, the 1986 ruling that forbade local authorities to "promote" homosexuality.
A coalition of children's charities issued a joint briefing paper to the Lords calling on them to support the repeal.
Bob Reitemeier, chief executive of the Children's Society, said after the vote: "Section 28 has acted as a barrier and prevented young people from receiving the support, help and respect they need."