I am not a very principled libertarian, and make no pretension of being one. In fact, I generally regard over-adherence to principle as form of irrational, dogmatic behavior. That's why I tend to try to tweak the parameters of what it means to be a libertarian, to take into account where the pure ideology fails in real life. The following are some observations, even if theoretical, on how cultural libertarianism, though not necessarily purely political libertarianism, tends to fall down at addressing issues that can have deep ramifications.
Scenario 1. The Elusive Wapiti brings up the possible dangers that having a large amount of estrogen and other female hormones might have on public health. If it can be proven beyond a reasonable doubt that such chemicals have these effects, then it would make sense from a rational biological perspective to ban birth control for women who don't have a compelling case for why they need it. Three good examples that come to mind would be women who cannot safely have any more children, women who are too poor to care for their own children, and women who need it to correct for a hormonal imbalance. Banning it for those who just want to control their ability to get pregnant would cause a dramatic reduction of the chemicals in the water supply over time, but would represent a serious reduction of sexual freedom for women. However, if it can be proved that this freedom is causing physiological harm to others, on a utilitarian basis, if nothing more, it should be restricted. Yet many cultural libertarians would have a very hard time accepting such a decision, even if it were proved to be necessary for public health.
Scenario 2. Not all religions are created the same. With Scientology you have an abusive cult that makes probably billions of dollars by sucking the life out of its victims. It is also an entity that has such unusual practices as suing critics for copyright infringement for distributing its "scriptures." In many areas that matter, it is a business that operates under the guise of religion, and has a sordid history of compliance with the law.
Then there is the issue of groups like Wahabists. These Muslims are working actively to sabotage the traditional freedoms of every Western country they infect. They are nothing less than violent and devious subversives whose goal is to eradicate the very freedom that libertarians of all stripes want to preserve or restore. There is no negotiating with them, and even down to individuals, it is dubious how any remotely free society would be better off having such people inside its borders, operating freely.
In both of these cases, cultural libertarians would be quite upset with a systematic attempt by a government to rationally crackdown on such dangerous groups, and remove their influence from society. This is despite the fact that it would be a small move to protect freedom to crackdown on their activities, as they are often focused on breaking down what freedom is left through means ranging from systematic legal harassment of critics, to fomenting violent extremism in our own borders.
Scenario 3. The media betrays basic operational security for our military, or one of our allies, in a way that doesn't get anyone killed, but that shows a deep-seated lack of concern for the lives of military personnel operating abroad. A good example recently was when the media revealed the location of Prince Harry in Afghanistan. By doing this, not only was Prince Harry's life endangered, but so were the lives of everyone in his unit because killing him would be a significant symbolic victory for the Taliban. No harm has come from this, but there was no public good served by revealing his location. However, if he, or people in his unit, had been killed soon after this because the Taliban immediately went into action, many cultural libertarians would have a hard time accepting moves by the government to prosecute and serverely punish every member of the media responsible for such a brazen, needless and harmful act against operational security.
Scenario 4. Children tend to do a lot better in many areas when they come from a two-parent household. That said, cultural libertarians see no evil in allowing single women to conceive based entirely on IVF, couples to spawn entire families out of wedlock, and homosexuals to have their own children through various medical practices. It is understandable that they would be hesitant about outlawing these things, as the Law of Unintended Consequences can have severe implications, especially when it gets into such a fundamental area of human life. However, cultural libertarians tend to refuse to acknowledge that these individuals are placing their reproductive freedom over nearly every aspect of the security and well-being of another human being's formative years. In effect, they are treating them like property, not like they are another human being whose rights matter, and who they are bound by natural bond to protect and sacrifice for until they are an adult by virtue of bringing them into this world. In general, cultural libertarians place no importance on the well-being and development of children in a libertarian society because to do so would be to limit the sexual freedom of their parents.
This list is mostly just a starting point. It's intended to be more of an honest critique of how cultural libertarians react in practice, rather than an attack on libertarianism itself. Anyone else have scenarios they think fit the bill?
As always, I am aware of the Law of Unintended Consequences, which is why I am hesistant about the government intervention in these cases except for number three. However, I think any rational person in the libertarian movement can step back from their prejudices and realize that all of these are problematic scenarios for at least one party involved, when it comes to their rights versus the more "immediate rights" such as sexual freedom, that libertarians tend to reflexively protect against any limitation.