There's no such thing as "gay rights", nor "women's rights", "black rights", etc. Ok, maybe I was trying to be controversial to get your attention. I can already hear the political Left crying: "You're a homophobic, sexist, racist and we should stomp in your face." Of course, this comes off harsh to those whose typical conception of rights are that of duties to other people, and not that of the freedom from doing things for other people. But the case is that only individuals have rights. In this sense, the gay person does have rights, but not because they are gay; they have rights because they're an individual, too.
No one – not homosexuals, transgenders, women, minorities, whoever – has special rights that supersede the rights of the individual. It's likely the case that these people do in fact believe that others should award these classes of people who are allegedly "victims" of prejudice the property of others, just as they already believe "rights" are rights to other people's property, i.e., essentially socialism as a right.
But if someone is disliked by another, or discriminated against, they cannot be said to be a victim unless their property rights have been violated. No one has a right to be loved by everyone or anyone, as sad and unfortunate as this may seem. Libertarians believe in natural, negative rights; or the right to be free from aggression against your person or property. This is opposed to the statist view of rights, that one is obligated to do things for others, involuntarily.
Discrimination, i.e., deciding who you associate with or not, is a natural right. It is not a crime to not do something for someone, such a not invite them onto your property; it's a crime, however, if they invade your property without your consent, and unfortunate, i'd say, if they're "legally" allowed to do this according to state-made "law." Freedom is, if anything, the freedom of association. The contrary is necessarily what the State enforces with its anti-discrimination laws, i.e., the assisting of crimes (violations of property rights), or the forced integration of people who wish not to associate with one another, helping to breed resentment among each other in addition.
It is for this reason that we're forced to associate with, via compulsory taxation, the "services" provided by the State (the military, road, or school monopolies, etc) that the libertarian rejects these "public goods", for they do not allow us to decide freely who provides our security, education and such. We're not allowed to discriminate against who provides us service as we would in a free market, or what these people who steal our property go to use it for, as we would be able to absent taxation.
Indeed, if it is so that anyone thinks a homosexual has a right to the product of a heterosexual, say, the cake baker, and therefore that the latter is forced to provide a service and accept the invasion of his property, then it is that they believe the "straight" person doesn't have rights; his rights to property, to exclude anyone as he sees fit, are violated to favor the non-existent "rights" of the gay person to enter his property.
So really, in this situation, it has to be decided who has the rights: the gay person who wishes to have the "right" to the services of another man; or the other man who wishes to have a right to not associate with another person. While giving the former the "right" to the private property owner's business means the property owner must lose his rights, allowing the private property owner to keep this right of excludability doesn't take anyone's rights, but allows both people to keep theirs. The business owner gets to keep his right to decide who enters his property, and the person desiring entry never had such a right. I know I would gladly leave if a business owner said "cis white males are not welcome here", and I couldn't imagine begging to exist in a place where I was unwanted anyway.
Giving someone a [positive] right they never had, such as a "right to health care", means someone must give up their rights unwillingly as a taxpayer. It cannot work both ways, where everyone has the right to another's property, for someone must be the one who gives up their property and someone must be the one who receives it. This is why libertarians have adopted the private property ethic, for it is the only universalizable ethic that everyone can hold at once without another losing their rights.
While I would agree that there may be something immoral about hating gay people, and for the record I personally do not, I yet see no legal problem if one wishes to do so, in so far as it is not acted out aggressively towards the property rights of the homosexuals themselves. Some might contend homophobia would lead to a crime, but this would be to accuse anyone of a crime merely for thinking something when they have not, and do not intend to, act it out. For this reason it's easy for non-libertarians to accuse libertarians of being "homophobic, bigoted racists", or whatever, because they cannot distinguish what we're making for a legal case from what we hold as our personal morals. Sure, we should maybe condemn racists, but we cannot punish them legally. When it is not an act of aggression but merely a psychological disposition, racism cannot be considered a crime; it's a distasteful feeling someone holds against another for whatever reason, and surely a very unfounded one at that, since, again, we're all individuals.
If you have discovered a "bigoted libertarian" (someone who practices non-aggression philosophically, although holding the preference of disliking a certain group of people: homosexuals, blacks, women, etc), then this person should be judged for their personal set of morals, and not for their libertarianism. Probably, you should call them a collectivist, since this would strike at the heart of their belief that they're individualists, since grouping individuals into a class of people for their skin color or sexual preferences is very much so collectivism. Concerns of social issues, though, are outside the scope of political philosophy, which seeks to define when violence is criminal or not, and so saying all libertarians are racists (because we believe in property rights) is the same thing as saying all vegans are socialists because you found one vegan socialist. Critique a homophobic/racist non-aggressionist for his homophobia/racism, not his avowal to non-aggression.
The libertarian must be pro-discrimination in legal theory, because libertarians are pro-property ownership, if anything. The right to property entails the exclusive right to determine its use, only as far as it doesn't prevent anyone else from doing the same. This might be considered the golden rule, or libertarianism 101. While this is true that discrimination is a right, I might suggest they still "shouldn't" do so in practice, but if they did would uphold that it's their freedom to do so anyway.
Seeing as the market wishes to provide to people, and to make a profit, regardless of sexual orientation or religious affiliation, it's unlikely such discrimination would be in widespread practice. If it is though, it should be anyone's right to exclude whoever they wish from their property in the same way that they could say "no gay family has a right to eat dinner with my family." Someone should be able to open a "straights only" bar if they wish, and as well, a "gays only" club. Surely even straight people who don't favor such bigotry will invoke their right to boycott it anyway, refraining from giving it business.
To conclude, homosexuals have rights, but not any special rights that stand above anyone else's. Rights are human rights, and these rights are to property and for this property to be free from aggressive invasion. Not inviting someone onto your property for whatever reason cannot be labeled aggression; it's someone practicing their freedom.