Indeed. Aside from the financial benefits, that is a large part of the push for gay "marriage."
Maybe 15 years ago, when I was a student at UC Davis, a lesbian wrote to the campus newspaper stating exactly what you said. Her family did not accept her as normal. According to her faulty logic, if she could only get married to her girlfriend and make the relationship legal the way heterosexuals legalize their relationships, her family would realize that she is just as normal as any heterosexual.
Tellingly, her argument did not contain any discussion of love--for her, the gay "marriage" issue was about being seen as normal, and had nothing to do with the actual relationship.
Normalizing perversion, which leads to criminalizing criticism of said perversion, except for the narrow exception Kennedy carved out for pastors.