As if my motives are some deep, dark secret. Obviously the reason I would like women to look at pictures of a developing fetus is because I think the raw facts support the pro-life position. I think it's odd that you use the word "anthropomorphize" to describe something with human anthropology.
Your position seems to be shaping up to be this: the government can only regulate the behavior of a doctor for medical reasons. Why? You said before that the state has some interest in fetal life, and brought up kidnapping victims. I'm having trouble understanding how a minor inconvience like being handed a picture is not justified by a state interest like that. That's not like asking to search everyone's home looking for missing children, it's more like if they put a picture of missing kids in the bottom right corner of a government form you have to fill out to register your property. What's the big deal?
I'm trying to understand what principle you are employing here. Would it be okay for the government to require a warning on cigarettes even if you did not find the evidence for health risks associated with tobacco convincing? What do you mean by "the facts have to be comprehensive"? How much evidence that spaking is bad would you need?
If OB-Gyns want to show women pictures of afterbirths, they have a right to. I can't see any legislature wanting to compel them to do that. If one did, it would be stupid, but I don't see how it would be unconstitutional.
Does the SD law force doctors to claim that they believe anything or does it leave the doctors free to say what they believe about the content of the message? My hypothetical picture-of-a-fetus law would leave the doctors free to say "My belief is that life begins at birth" or even "I believe this is a picture of a Volkswagen."