"What if the sperm donor is a hard-core moonbat of some kind?"
Then the hospital should not have donated the sperm.
Now the father has the right to see that this child is raised as he sees fit irrispective of his background.
The clinic shouldn't have "donated" the sperm to an unauthorized recipient, no matter what the qualities of the man who produced it. And I respect a clinic which does not deny services to someone because s/he fits their personal definition of a "moon bat". Remember, the clinic did not select this man to be an anonymous donor; he was there to provide sperm to his fiancee, not to some woman he'd never met. I would hope they would screen out people who would widely be regarded as "moonbats" as anonymous donors (but in practice, clinics don't get involved in selecting sperm donors -- anonymous donor sperm comes from independent sperm banks, with both the bank and specific donor selected by the female patient).
And the mother?
Should she not be allowed to raise the child as she sees fit, irrespective of the desires of a total stranger she never wanted to be connected to? Since they resorted to an anonymous sperm donor, instead of a friend or relative, I assume they didn't want any extra legal or emotional entanglments.
I don't believe either one has a greater moral claim to the baby.