How about this as a general rule, just to make things easy for everybody:
When religious liberty (e.g., the right to believe that homosexuality is a sin) conflicts with personal liberty (e.g., the right to adopt), personal liberty always takes priority.
Why? Because your right not to have your sensibilities offended is less important than everyone else's right to life, liberty, and the pursuit of happiness. Period.
(Oh...and in cases like this one, where what "religious liberty" really boils down to is whether or not you're being funded by the government, I'm just going to suggest that you go right ahead and fuck yourselves. OK? Thanks for reading!)