As Thomas Aquinas and St. Augustine said, an unjust law is not a law. Protecting our borders is just law. Requiring proof that one is a natural-born citizen to serve as President is just law. Paying off political contributors by requiring that citizens or residents use their product is not just law. Nor (for another example) is abortion on demand. There is no divorcing law from morality; law has no purpose other than to serve morality.
Unjust laws are inconsistent with law itself, and render a legal system self-contradictory. Not only are people who defy unjust laws not doing wrong, they are improving the system by targeting its faulty parts for elimination.
Here is Aquinas:
"Laws are unjust in two ways: First, they may be such because they oppose human good. . . This can occur because of their end, when a ruler imposes burdens with an eye, not to the common good, but to his own enrichment or glory; because of their author, when someone imposes laws beyond the scope of his authority; or because of their form, when burdens are inequitably distributed, even if they are ordered to the common good. Such decrees are not so much laws as acts of violence, because, as Augustine says, 'An unjust law does not seem to be a law at all.' Such laws do not bind the conscience, except perhaps to avoid scandal or disturbance. . .
"[L]aws may be unjust because they are opposed to the divine good, as when the laws of tyrants lead men to idolatry or to something else contrary to divine law. Such laws must never be observed, because 'one must obey God rather than men.' (Acts 5:29)." (Summa 96:6)
And preventing people from Cervical Cancer is somehow harmful? What 'good' does Cancer serve?
Would you be opposed to a mouthwash that prevents tooth decay as well? I don't feel that having my teeth rot out is in anyway contributing to the 'human good'. This is simply a byproduct of living in a country with the great capabilities of growth in medical science. BTW, the mouthwash is now available in England - and if there is a country on the face of the planet that needs this, it's England. But, next time I'm in London, I'm gonna get a shot of this.
Will this become mandated by law? No, because rottent teeth are typically not life threatening. However, Cervical Cancer is very much a life threatening illness. If we can prevent it, don't we have a duty to do so?