I mentioned this on Universal Hub, but thought I'd mention it here too. I'm fairly sure the first amendment doesn't mean taxpayers can't pay for healing that has any religious content. I use a lot of religion and spirituality in my practice, and I get reimbursed by public and private insurance, but I also don't do anything that's not congruent with the standards of the licensing board and ethics committee and so forth.
The real problem with Christian Science healers is that they aren't practicing anything remotely resembling scientifically informed and/or evidence-based practice, thus can't be licensed by the state boards. Wherever they get their training from isn't approved as sufficient training for any sort of healthcare license.
Sure, people are free to go to them, but slapping "healer" or "practitioner" on your business card doesn't mean insurance should pay for it. I'm fine with public or private insurance paying for a licensed therapist who uses Christian/Jewish/Buddhist material within the context of ethical and evidence-based therapy with clients who share this religious view and find it helpful in increasing their understanding of their world. I'm not OK with someone going to get prayed at (and told to stop taking the meds that make them not psychotic) and this being called professional healing that the public should pay for.
I feel like the licensing boards are fairly generous in terms of what they consider to be professional medical-model healing, and prayer alone certainly doesn't cut it. Personally, I find that prayer helps me with my mental well-being. So does having pets. So does skiing. I think it's fairly obvious to any reasonable person that the government should not pay for my synagogue membership, my pets, or my ski trips. And that the government should pay for me to go to a professional licensed therapist who might share my religious preference or other life interests and who might talk to me about how these are things I can use to increase my satisfaction with life.