"I support safe vaccines, it just so happens that I don't believe that any vaccine is safe and I am not willing to trust the medical system to evaluate vaccines for safety and will continue to insist that all vaccines are unsafe" has the net effect of not supporting vaccination at all.
In practice, this is always what so-called anti-vaxxers believe. None of them actually oppose the concept of vaccines out of some kind of ideological principle. It's always specific concerns about actual, specific vaccines that exist in the real world.
That's being extremely generous, many people with anti-vax beliefs have not arrived there through careful, rational consideration of anything specific.
To be fair, same can be said of pro vax people. Blind belief into what science have become is perhaps more dangerous than blind disbelief.
It amounts to noticing that few if any of the people you know or are acquainted with through two or three removals from personal contact, have suffered or died as a result of using said technology, and basing your own confidence solely on this privileged form of hearsay.
It sounds like something that should not work, but actually does a pretty good job as a high-pass filter for safety.
"Vaccines could be safe if we can demonstrate that the moon is made of cheese" is the same as "vaccines are all unsafe."
And additionally, would you think it is a good idea to generalise here?
If you would dare to explore, you would find it's based on scientific approach, where trials and statistics matter.