OP, you're using somewhat of a misnomer with "pro vaccination". "Anti-vaxers" isn't truly about not wanting vaccinations - it's about something different.
If there were multiple vendors who created an open-source recipe for various vaccines, and I could get them and even have them tested for ingredients, that would be great! At that point, it just comes down to the merits and philosophy of whether a particular vaccination works. There wouldn't be any question about what was actually in the "vaccine".
So, authoritarians like they do with so many other things - say that if you don't want gov't to do it, you must not want to do it. For example: "You don't want to give out welfare? You must not want to help people". Response: "Nooooo, I can help far more people FAR more efficiently then your big bloated system, where you take a very slice of the pie". Similarly, when an authoritarian says: "You don't like our mandated inoculations with these secret chemical? You must want to hurt your children!"
ANYHOW, so along those same lines - what do vaccinations actually look like? They are closed-source, are not independently tested, and then... government suddenly has a very strong opinion about you taking this shot. They think it should be mandatory that you take a shot of something... which can't be verified. That is a very, very bad combination.
"Oh boy, what do you think is in there? You think companies would give us bad vaccines with other stuff in it?" First of all, with mandatory vaccinations: they absolutely could, and you couldn't do a thing about it. That's why mandatory vaccinations are bad. Plus, malicious third parties could also taint our supply - and on-and-on it goes. But as for my strawman question, all you need do is spend 3.5 minutes researching the history behind common vaccinations. Start with the simple influenza vaccine that is given each year - see how many people it kills.
Next, look into Jonas Salk. He used monkey brains in his polio vaccinations, where there were a lot of monkeys infected with Simian Immuno Virus (SIV). He then vaccinated something like 20 million children in the Congo, to become this world-renowned "hero"! A few years later is where the mutated form, HIV came from - exactly the same region, and a direct mutation of SIV. Because of lack of paperwork, i's difficult to prove - but it's certainly some damning circumstantial evidence! Look at modern day vaccines with mercury in them! Mercury is highly, highly toxic to the human body - yet it's in our medicine?
My point is, just because someone isn't pro (mandated, unverifiable, untestable, government-enforced) vaccine, doesn't mean that they don't want to protect children and be healthy. It more likely means that they don't think it's appropriate for another person or organization to physical force you to take medicine which has a long and notorious history of harming people. Something to consider...