As a general view, absolutely not. However, I fail to see how this is different than any professional licensing scheme.
I am not a doctor. Should I be able to publish a book explaining how to set your child’s broken bone without the need for pesky doctors and hospitals so you can save money?
Almost universally, states have decided that for the protection of the citizenry, there must be minimum standards that doctors, lawyers, hairdressers, plumbers, etc. have to have achieved before they will be permitted to ply their respective trades to the public. And as a result, there will be certain books that will not be permitted to be published and certain speech that would be unlawful.
This is part of the general police powers that states have exercised for hundreds of years to protect the health, safety, and morals of the public.
However, I do understand your concern. In this instance, the state is not saying that only qualified people can give advice on “conversion therapy.” It is saying that conversion therapy is so flawed and such quackery that NOBODY can advocate for it without facing civil liability.
As I said, I could see how an aggressive implementation of this law could run afoul of free speech or freedom of religion concerns, but if we take the Legislature at its word, then this law should only apply to purely commercial speech directed at inducing a person to try “conversion therapy” with the implication that there is valid science behind this therapy. Although, I’m not sure I would support such a law since we allow all sorts of other forms of medical nuttery to be permitted, I don’t see it as a constitutional crisis where books are being banned.
The law however, should not apply to preachers handing out Bibles and saying that if you are a practicing homosexual, you need to “choose” to stop. Nor should it ban the publication of a book by a “former” homosexual that claims to have been “cured.” That would clearly be a violation of the First Amendment, and I hope the courts very narrowly construe this law.
