What are "anti vax statistics"? Do you think people who refused to take the COVID vaccines were making up their own data from whole cloth? I never saw that. What we do see is that the stats presented by health authorities are often mangled by inappropriate methodologies that appear to be picked in order to arrive at pre-chosen outcomes. When the raw data is obtained and re-analyzed correctly, we get papers like this one:

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4125239

"The excess risk of serious adverse events of special interest surpassed the risk reduction for COVID-19 hospitalization relative to the placebo group in both Pfizer and Moderna trials (2.3 and 6.4 per 10,000 participants, respectively)."

In case you're the sort of person who evaluates arguments based on credentials not merit, the authors of this paper are all from universities or health services. One is an editor of the BMJ. One is a professional statistician and epidemiologist (https://en.wikipedia.org/wiki/Sander_Greenland)

You assert that the modern COVID anti-vax movement is "conspiracy driven". But there are two problems with this argument:

1. It's not really true. Refusal arises because public health officials have repeatedly lied about the vaccines, saying things like they are 95% effective against infection, or that they'll turn people into "dead ends" for the virus. That second one was the rationale for mandates and it was known to be false from the start - the trials never showed any such thing and they had no reason to believe this given that non-sterilizing vaccines are common. As for the first, the governments that publish actual case rates by vaccine status show that they have effectiveness in the minus 300-400% range i.e. vaccinated people get COVID at a much higher rate than unvaccinated people. So that wasn't true either.

2. Even if it was the case that it was all driven by conspiracy thinking, so what? It's already been proven beyond all reasonable doubt that public health leaders engaged in multiple conspiracies throughout COVID, e.g. virologists writing in private emails that they thought the virus looked like it'd been modified in a lab, and then days later signing an open letter saying the opposite. Or public health flipping from "masks are useless" to "masks are essential" overnight without any new science to drive it.

Given this history the argument that anyone proposing the existence of a conspiracy is illegitimate is, well, extremely naive.

"The risk of course is when the vaccines are defective such as with The Cutter Incident in the 1955. This was probably the root of the modern anti-vax movement"

The anti-vax movement existed from the very start. Research the history of the smallpox vaccine. Parents were choosing to go to prison for violating mandate laws rather than let their children be vaccinated because they'd seen that vaccinated children came down with actual smallpox at much higher rates than expected. Just like today, public health refused to countenance the possibility that there were any possible problems in the vaccination process. They never change. It's a psychological issue.