I am of the opinion that responsible couples who give up their children for adoption should have the right to request a restriction in the religion and sexual preference of potential adoptive parents.
Now that is an interesting question. Should birth mothers be allow d to dictate by who and how their child will be raised when given up to adoption? You mentioned "responsible couples" in your post, but I doubt there are many responsible couples giving up kids for adoption. Having birth parents who were neither responsible or a couple is kinda how these babies ended up being adopted.
I would allow for input on religion and at least a lower middle class standard of living.
To be honest, I know quite a few adoptive parents who are more than dysfunctional but have good careers and nice homes.
You can be successful, yet irresponsible, or just downright evil.