So it's important to take as your facts about vaccines the general scientific consensus. Not what any single study says, not what any single expert says no matter how credible, not what you want to be true, not what's popular in your culture, not what aligns with your political or religious beliefs, not what a trusted friend tells you—not even what I tell you—but what the totality of the greatest intellectual enterprise in human history currently agrees to be our best understanding. The current consensus understanding about vaccines is not at all controversial, despite what other pundits may tell you. The facts are clear: vaccines work. Being vaccinated greatly reduces your chances of getting and spreading the disease for which you are vaccinated. No vaccine is 100% effective; some are more effective than others, but all of them work pretty well. The best examples are smallpox and polio. Smallpox killed an estimated 300-500 million people, and is now extinct in the wild. The last naturally occurring case of what was once the scourge of humanity was in October 1975, a two-year-old Bangladeshi girl, Rahima Banu. Polio used to fill hospital wards with children in iron lungs, and is now eliminated everywhere in the world except a few places that fight vaccination programs for religious reasons. Probably the least effective is the annual flu vaccine. Flu is a difficult target, and our aim varies. But even this vaccine has a risk-reward function that favors getting vaccinated for most people (there are exceptions your doctor will tell you about). And flu is not just a nuisance—it really kills people. The Food Babe's advice to “encounter the flu naturally” is uneducated, dangerous, and irresponsible. People encountered smallpox and polio naturally too, that's why we invented vaccines.
Even among those who accept the scientific consensus make simple errors of mathematics in evaluating the likely outcomes of their choices. The primary mistake is to rely on simple black-and-white thinking instead of probabilities. The world is a complex place, and the most complex parts of it are biological things like humans and viruses. Simple statements like “A causes B” or “A prevents B” are generally not an accurate picture of how things happen in biology. Randomness plays a big part. Many people who never smoke get lung cancer, and many people who smoke all their lives don't. That doesn't mean there can't be a causal relationship. There's a very strong one: smokers are 10 to 20 times more likely to get lung cancer (men more likely than women, for reasons still unknown).
Some people who get vaccinated still get sick. And many people who don't live long healthy lives. That doesn't mean there's no causal link. Most vaccines are a slam dunk: The introduction of the polio, measles, mumps, and rubella vaccines reduced the total cases of those diseases by over 99%. Pertussis (whooping cough) was reduced over 95%. Because it's somewhat less effective, recent outbreaks of whooping cough have arisen in communities with low vaccination rates. Some are far less effective, but still useful: The yearly flu vaccine reduces flu rates by about 60%.
People also don't properly compare the risks of multiple choices. For example, many people at the blackjack table refuse to hit a 16 when the dealer shows a 10, because the risk of busting is high. They are correct about that: hitting will cause you to lose 53% of the time. But standing will cause you to lose 54% of the time. Hitting is risky, but standing is worse. You hit not because you want to win, but because you want to lose less.
Vaccines can have real side effects. These too are variable, random, and unpredictable. Most are mild (pain at the injection site, fever, rash), but many are indeed serious. That's why the US has a fund for compensation of victims of vaccines. The risks are real, but just saying that vaccines are “unsafe” because there are risks isn't telling the whole story. There are two choices, and neither is “safe”. Reality, which is under no obligation to make life fair, simply doesn't offer any safe option. You have to choose one risk or the other: hit or stand, either vaccinate and risk side effects or don't vaccinate and risk disease. Making that choice requires real numbers and real judgment about the seriousness of the consequences. The MMR vaccine, for example, has caused anaphylaxis (a serious allergic reaction) in patients because it can contain egg proteins and gelatin. But the numbers are tiny: most doctors have never seen a single case, just as most have never seen a case of measles or mumps since vaccines began.
The final risk/reward calculation involves a branch of math called decision theory. This is a pretty simple case: the tiny odds of the two bad outcomes (disease, vaccine reaction) have to be multiplied by the “badness” of each outcome to get what's called the expected value of each choice. This math pretty heavily favors choice one: vaccinate. The downside of disease is much worse than the downside of a reaction to the vaccine, and the odds of both are tiny.
Even if you accept the facts and the math, there are still people who decline to vaccinate for what they believe are ethical reasons. I value freedom, and I'm quite sympathetic to those who claim the right not to vaccinate themselves even if I disagree with their reasoning. But even dedicated libertarians acknowledge an important limit to freedom: your freedom to swing your fist ends at my nose. When your choices affect others, I have a right to object and a duty to speak up. We are of course outraged when a Muslim family kills their daughter] for being raped to save the family “honor”. I see no moral difference between that and Christian Scientist parents who kill their daughter by denying necessary life-saving medical care. Both can and have been put in jail, and rightly so. I am not suggesting that failure to vaccinate your children rises to that level, but the issue is similar. Simply crying “freedom” is not sufficient moral justification for endangering the lives of your children and those they encounter. I do believe it is entirely appropriate for schools, for example, to refuse to enroll unvaccinated children. They too have the freedom, and perhaps even the duty, to protect other students from your choices.
Some people have the feeling that not acting has fewer moral implications than acting. A classic example is the trolley problem: you see a train racing out of control toward five people some evildoer has tied to the track, and who are too far away for you to warn. A switch near you will divert the train onto a side track where a single person is in the same predicament. Do you throw the switch? Even though throwing the switch will save lives, somehow not throwing the switch seems less blame-worthy to many. Likewise, they believe that if they vaccinate their children and who then suffer side-effects, that is somehow more blame-worthy than if they decline to vaccinate and they get the disease. But the choice is conscious either way: avoiding the “active” choice is not being conservative, it is moral cowardice.
I can't make the choice for you. But the picture above should make it clear what my choice is, and I urge you to use the right tools in making yours.