I’m not sure the first amendment issue is the best argument. The Supreme Court had recognized limitations on the first amendment not being absolute. I would be concerned that the argument maybe that misinformation would be akin to the proverbial yelling fire in a crowded theater.
While this law is clearly immoral on its face and government overreach, I would tend to think the better argument is that there is already a pathway for relief in a malpractice suite. If a physician commits the act of malpractice which would clearly include misinformation, the remedy would be a civil lawsuit. No need for this law which would be capricious and whimsically enforced.
I think this is the dagger argument in the heart of a court challenge to this law.
I tend to agree - to a degree. Because doctors are licensed, they don’t have free speech. I used to be a real estate agent. We were licensed. If I said, in an ad, that a house was in a homogenous neighborhood, or said it had a “family room”, that was forbidden. I could have lost my license. But the average person can say it at will.
So the key is the use of the word “consensus” in the statement. That is patently absurd. Those who embraced the consensus, kicked a rather famous inventor out of the Catholic church a few centuries ago because he disagreed with the consensus.
OTOH, if the doctor really IS giving deadly disinformation, that is what civil lawsuits are for, as you pointed out.
This is just another reason to get out of California.