1. To begin with, the statement and follow-up question insinuates that there is a great number of parents refusing to vaccinate their children out of some sort of "fear"; however, unless someone can point out some actual data to support that, I'm not buying it. When you look at the data from the CDC (see the link, not sure how to cite it), you can see that for most vaccines, upwards of 90% of children ages 19-36 months are vaccinated. For measles it 91%. Of the children who aren't, surely there are reasons other than "refusal" as to why they are not vaccinated. From this, we can infer that the "anti-vaccer" movement isn't as huge as the media makes it to be.
But to answer the question, many parents refuse vaccines (and other medical treatment) for religious reasons, while others refuse certain vaccines because they have a misguided belief that the vaccine causes autism. One of the reasons that there is a group of people who believe that vaccines can cause autism is due to the fact that autism has risen from 1 in 150 children to 1 in 68 children since 2000 (Rodriguez, 2015, par 4). The level of vaccines has risen during the same period; however, as we all should know, correlation does not equal causation. The increased autism rate could also be caused by less cases of autism going unnoticed.
https://www.cdc.gov/vaccines/imz-managers/coverage/nis/child/data/tables-2014.html
2. The argument that the widespread commercial use of antiseptics and disinfectants can hurt American health is in part due to the microbial resistance to antibiotics. Antiseptics and disinfectants are used for a variety of topical and hard-surface applications and are essential in the aid and prevention of the spread of bacteria. The chemical agents found in these products have a broad spectrum in the kind of bacteria they kill. Because of the widespread use of antiseptics and disinfectant it has brought about the development of microbial resistance, in particular cross resistance to antibiotics.
If we constantly live in a sterile environment killing off the weak bacteria and letting the stronger ones get stronger and then we do get sick the antibiotics will have no effect on them. In a sense our cleanliness is making things worse.
Antiseptics and Disinfectants: Activity, Action, and Resistance