For starters, even though the vaccines may be free to the public, governments still need to purchase them from the pharmaceutical companies themselves. Making them free to consumers is called "subsidising".

Secondly, "vaccines cause autism" is one of the most common link anti-vaccination proponents will make. There are a few reasons for this. The most famous is Andrew Wakefield's publishing of a paper in The Lancet (a prominent medical journal) that linked the MMR vaccine to the onset of autism-like symptoms. His study was not scientifically, ethically, or methodologically sound for various reasons (it's a long story). Since the paper was published (and eventually retracted), several more have been written that consistently find no link between vaccines and autism.

The point you talk about is known as "herd immunity". This basically means if a high percentage of the population are immune to a disease, that disease won't spread so easily through the population - enough people will carry immunity that protects the whole herd. This is important because there are a small percentage of the population who 1) cannot receive vaccinations, or 2) do not receive vaccinations. The former is usually to do with certain medical conditions or age. The latter is usually due to moral reasons, but a small proportion of these people simply remain "unvaccinated". These people objecting on moral grounds are the "head scratchers", as they literally put lives at risk by their inaction, despite overwhelming evidence to the contrary. In fact, one of the reasons why vaccines are subsidised (often fully) is to protect against the substantially higher public health cost of a disease spreading through a population (think of Ebola).

As a final point, a lot of anti-vaccination advocates will argue that autism diagnoses increased since more people started getting vaccinations. A statistician or scientist will tell you that this is not satisfactory evidence that vaccines cause autism. It may be due to a "missing variable" - such as changes in the diagnostic criteria for autism, and better recognition and diagnosis of autism. There may be other reasons for increased prevalence, however we can say with a high level of confidence that it is not due to vaccination.