To vaccinate

People have issues with vaccinating their kids. To be frank, I don't understand why. If it's because of autism, read this; if it's because you're relying on herd immunity, read this study or an explanation at Science-Based Medicine; if it's "too many, too soon", read this study or an explanation at White Coat Underground. The only concern I find putatively legitimate is the use of animal products, and that's by far the argument I've heard the least.
I'm a molecular biologist, which means that I know a whole lot about not very many things. One of the many things that has escaped my thorough understanding is how vaccines are made. My basic understanding of the process is that a few cells are taken from an animal source. They're cultured in a sterile environment and infected with a virus. The cells grow and are fed growth factors to propagate that virus and make tons of it. The mixture is separated into cellular and viral components. Sometimes the virus is partially killed or attenuated then mixed with stuff to become a vaccine against that virus.
Based on that understanding, it's hard for me to see how cellular components could get into the final vaccine mixture. I think when parts are separated out, it's done by centrifugation, which means that the mixture is spun so quickly that everything separates into layers based on relative density, a parfait with cell chunks in one layer and viruses in another. Some anti-animal derived vaccine folks are upset about pieces of chickens or whatever getting injected into our babies. These same folks claim that some vaccines are also made using fetal cell lines. Now if separation of virus from everything else is straightforward in the vaccine-making process, it doesn't seem like this should be a concern with regards to what's being injected. I get that this debate can go further back, to ethical issues with abortion, but that's not what I want to discuss here. Bottom line, I don't think there are bits of other babies in vaccinations.
But I said this was a putatively viable complaint. I said that for this reason: what if there are already viruses in the cells you're using? Now I'm sure vaccine manufacturers have to quality control like it's going out of style. A quick search on the CDC website for "vaccine" tells me they're quite aware that vaccines are a big deal. I work at a large research institution and I have to have 12 people sign off every time I blow my nose. But, hypothetically, let's say they don't catch something. Is it possible that they harvest cell lines from a cow that has a virus, and that virus slips under the radar, and that virus propagates with the intended virus, and now you have a vaccine that contains Crazy Cow Virus? These must be concerns, as the CDC has a phrase for them: "adventitious agents". And there is a body of research in full swing trying to produce vaccines that are free from animal products (possibly because it is a real concern; possibly because it is a real market. Eh? Money, you say?). I'll be reading up on this.
For now, maybe, maybe SOME of the anti-vax people have A reasonable complaint. Or... maybe they're kind of crazy.