As same-sex marriage is argued before the Supreme Court, conservatives are dragging out a 2012 study by Mark Regnerus, suggesting that parents who have same-sex relationships are bad for children.
Where to begin? To start with, the benchmark is intact biological families who are still intact when the children are surveyed, at age 18 to 39. A lot of heterosexual families would fail to clear this bar.
Same-sex parents are described as any that ever had a "romantic relationship with someone of the same sex", according to the child. This over-counts those that preferred same-sex partners.
This captures the climate for households formed 18-39 years ago, not the present. The stigma against same-sex households was greater then.
The "parents who have had a same-sex relationship" mostly came from failed opposite-sex relationships. Almost half were originally married to the biological father. Only about 20% were from households where the biological father was neither married to nor living with the mother.
To understand the limitations of the study, consider that it would classify Kelly McGillis as a lesbian mother, even though her daughters spent most of their childhood in a conventional heterosexual marriage.
Life is complicated.