Merely encouraging people not to vaccinate via educational and political communication without purporting to provide individualized medical advice is probably not the practice of medicine and protected by the First Amendment's protections for freedom of speech, rather than constituting medical malpractice.
Also, many anti-vax individuals (I couldn't quote a percentage) do so out of religious conviction and are protected not just by the freedom of speech in the First Amendment, but also by the free exercise component of the freedom of religion under the First Amendment. Generally speaking, it is harder to find a legal grounds for disregarding the free exercise of religion than it is to find a legal basis to regulate otherwise free speech.
For example, commercial speech is subject to more rigorous regulation than private political and educational speech, which is why there are no private businesses taking anti-vax positions in their advertising.
The theory is that courts are not in a good position to make general determinations of the truth of policy positions or statements about general truths as opposed to what happened in a particular transaction or occurrence. This is in part because a ruling by the right court at the right time can preclude the correctness of its determination from being revisited indefinitely and from time to time, accepted conventional wisdom and scientific consensus at one time are revealed later on to have been wrong with more discussion and investigation. I think that this is unlikely to be the case in the vaccination area, but the whole point of the First Amendment's protection of these kinds of issues is that we can't know in advance what will continue to be widely accepted and what will turn out to be mistaken.
But, if someone in a medical diagnosis and treatment profession (e.g. M.D., D.O., physician's assistant, or nurse), were to advise a patient in a capacity as a medical care provider not to vaccinate, and as a result that person's child got sick from a disease that vaccination could have prevented, there probably would be medical malpractice liability.
A somewhat similar issue arises when health insurance companies or government agencies set rules on providing care. In those cases, it isn't uncommon to have a physician or other medical professional placed on a committee or in an office such as medical director, with that person making the call and exposed to liability although not in the same way as a treating medical professional. A case about a month ago found malpractice by an insurance company's medical director (the company was United Health) to be a huge liability for both the medical director and the insurance company.