Here are two links that will answer your thoughtful question...
"Opting-Out” of HPV Vaccine WILL NOT WORK for Many in Texas"
The legislature had made law over the prior 10 years that made it nearly impossible for most people to opt out. The application to opt out was made easier by the Governor, one of the reasons he got criticized by the medical associations.
http://wingright.org/2011/08/07/dose-of-reason-perry-and-gardasil/
So, in other words, it is much easier to get out of than any other required vaccination? I had a son who had a bad reaction to MMR shot and was hospitalized when he was young. They kept trying to give him the shot again every year. I went through a lot more stuff than listed at your link every year he was in school to keep him from getting it and I even had documentation of his bad reaction to it. He was never dropped by any of our doctors or had any thing else happen due to his lack of MMR immunization which is required everywhere unlike Gardasil. I would take everything that site says with a grain of salt.