A completely libertarian society is unlikely to be achievable - some “liberties” necessarily impinge upon the other liberties, such as the freedom of a murderer or a rapist to carry out their intentions - this negates the liberty of their victims. The “liberty” of some wealthy moguls to accumulate ever more wealth necessarily impinges upon the liberty of other members of society to obtain an equitable share of said wealth. From what limited exposure I’ve had to US Republican policies, they seem to focus upon preserving the liberties of the wealthy few rather than increasing those of the needy many.
Instituting an optimally libertarian society depends upon reaching a majority consensus upon which liberties are to be valued, and which are to be denied. Another good example is the relatively recent case of the publication of satirical cartoons of Muhammad - to which the response of some Muslims was very violent, and that response led to a fearful retreat by the Western press. People do have a right to feel offended, of course - but to what extent does this imply an obligation, on the part of others, to care about such offence? Certainly it would be difficult to put the case - at least, in Western society - that merely feeling offended is somehow a justification for threatening the lives of those perceived to have caused offence.
Be that as it may, it’s fair to say that prostitution may or may not be a situation that compromises the liberties of those involved. Is the liberty to pay for sexual intercourse a liberty that ought to be valued by society? It’s undoubtedly true that many women are coerced into prostitution through straitened circumstances - often brought about by the very same unequal distribution that results from the preservation of the “liberty” of some to accumulate obscene levels of personal wealth. But it’s also the case that there are some individuals who enjoy sex work and appreciate the ability to make their living doing something they are demonstrably good at. Should this latter group, whether it be a minority or not (and it almost certainly is) be denied this opportunity to pursue paid employment, and thus pay their taxes, pay for education, accommodation, or the support of any dependants they may have?
As far as gay marriage is concerned, it seems unlikely that allowing homosexual couples to contract legally binding and socially sanctioned unions will in any way impinge upon the liberties of those who dislike homosexuality on principle - such people are quite free to ignore something that is not their business anyway.