For me, whatever a child's interest is prevails.
If LGBTQ people wish to adopt a child, and it is in the child's interest to be adopted by them, that's fine. And if it isn't, too bad.
I am not sure if the choice as described is between life with an LGBTQ couple or life in an orphanage. It sounds like the choice might be between two sets of adopters.
LGBTQ people want to disqualify their own lifestyle as a matter for consideration in adoptions. That's to say, if a child has the offer of straight and LGBTQ parents, they don't want their LGBTQness to be considered.
I don't think couching the question as being about limiting the adopters' "rights" is a sufficiently complete one. Every case involves at least one child, whose rights matter more to me. Adoption agencies should be allowed to make judgements about suitability.
Also, I think it would be reasonable for an agency to distinguish LGBs from TQs if they wish, if the child's interest is to do so.
On the other hand, I would suggest adoption agencies should not be permitted to apply religious reasoning in their choices of adopters. The Bible isn't an adoption manual. It isn't a means by which to distinguish parents who can adopt from those who cannot.