I know this is a heated topic of debate
This is exactly what uncertainty propaganda is about, pretending that it's a legitimate debate and trying to agitate. It's not sensitive because vaccines are dangerous, but because of the overwhelming evidence for their effectiveness at managing epidemics and the impact on society anti-science, anti-health management campaigns have, the harm caused. This means that conspiracy theorists harm society by pushing fear mongering propaganda claiming that vaccination harms. It also is institutional distrust propaganda, something weaponized by fascists for post-truth populism. The latter may include forcing quackery down your throat, something non-effective or even actually harmful. Meanwhile, the actual problem, a viral epidemic, for instance, is not being properly addressed.
Also important here is the fact that it's HPV that is being promoted (HPV vaccines being attacked), because it's a virus that's being used to blame and limit women freedom (addressing the problem increases their freedom and is perceived by patriarchy to "promote immorality" (not promoting subjugation))... I've heard the "sex practices causing cancer" arguments confusing HPV into it. They do the same about abortion. Even contraceptives... I've heard a teacher tell a student caught with a condom: "you'll catch AIDS!" when ironically, condoms when properly used are effective against AIDS transmission, precisely. It's the same old "sex is only for conception" nonsense.