It is not worse than 'just sin'. I can think of things far more detrimental to a child's health than two carers who are the same sex and happen to share a bed. How about rape, molestation, cruelty, beatings, verbal abuse, domestic violence, substance abuse, alcoholism, neglect etc etc.
Children aren't being harmed by it anymore than the knowledge that people DO have same-sex relationships is harmful. They find out they have parents who are homosexual and they deal with it. That's what children are like. Perhaps they may become a more tolerant person for it.
It won't influence the child anymore than the moment the child discovers a homosexual relationship anywhere in his/her life. He, or she, will make their own decision and have their own sexuality.
Kids from same sex homes have no discernible disadvantages in health, social skills, self esteem or emotional regulation. They actually seem to be more physically healthy than kids in straight relationships.
The USA, in general, just seem to have a really big issue with this PARTICULAR sin. If it were a kid being brought up in an unmarried straight home, that's not so bad. Or a kid being verbally abused or treated badly, well it's not so bad, pray and it'll be fine. But a kid with same sex carers, it's like the child is being beaten and tortured.
I'm not saying it's inherently natural for two people of the same sex to be parents, but I can think of much, much worse people to look after him or her. Much worse.
I'd rather a kid in a stable gay home full of nurturing and affection, than an Irish convent, for instance.