Let me clarify my question.
They are not persecuting him for no reason. According to him, they are persecuting him because it is dangerous if the public does not get vaccinated, even though there are not enough safety studies. Is that a legitimate consideration on the part of the Ministry of Health?

I understood that this was the question, and I answered it. If they have no scientific basis and what he says is a defensible position, there is no justification whatsoever for persecuting him. Isn't that obvious?

I don't think that's obvious.
They can argue that even though there are no meticulous safety tests, there are correlational studies showing a connection between lack of vaccination and illness, or studies showing higher infection rates among the unvaccinated, and so on. These could seemingly justify the following claim on their part: "Even if there are no studies showing that the vaccines are safe (studies that meet standards of causality), we do not want the public to know this, because there are indications that non-vaccination may be dangerous both to the unvaccinated and to those around them. Therefore, we would prefer to keep this information back in order to prevent non-vaccination, and anyone who publishes such information publicly endangers public health, even though he is not lying."

They can argue lots of things. So what?

My question is whether such a claim is justified, or in other words, whether considerations of public health can override freedom of speech that describes something true (assuming they did not refute what he said).

But that is exactly the dispute—whether this is really about public health or not. According to your suggestion, you could silence anyone who, in my view, is wrong. You're against the war, or in favor of a peace agreement with the Palestinians, or in favor of raising taxes, or against red traffic lights, or anything else—and I will silence you because, in my view, you are endangering human lives.

But it's not exactly like that; it's more complicated.
After all, he is pointing to problems in the studies in terms of causality, while they are pointing out (in the hypothetical scenario I presented) correlational studies. So they argue that even if we do not have knowledge of causality, it is better to be cautious. His emphasis on the lack of causality, from the Ministry of Health's perspective, may endanger the public, and that is enough in their view to try to revoke his license.
This is not just a dispute about public health, but also about the public's right to know. The Ministry of Health, because of public-health considerations, prefers that the public not know. Gil, because of considerations of the public's right to know, prefers to publish reliable information that raises research-based doubt and that may (assuming there is causality between non-vaccination and illness) endanger public health.

I'll write one last time and with this I'll end it. A scientific debate can take place on any subject. And people will decide whatever they decide and bear the consequences. That's all. Even if the Ministry of Health were clearly and scientifically right, there is still no justification whatsoever for persecuting someone over saying otherwise. He does not believe the scientific/medical establishment, and that is his right. That's it, I'm done.