Rand Paul thinks it should be okay to fire LBGT people because other people could hire them.
This is actually not surprising because, in the Paul family's flavor of libertarianism, individual liberty fares poorly if you are a minority or vulnerable in any way. And that's because they believe that everyone is a free agent and thus equally free. Real world power imbalances are not acknowledged in their theoretical model, therefore every dispute is a fair fight and we don't need government to referee. As many others have already mentioned, he similarly objected to the 1964 Civil Rights Act.
It's even less surprising since it is a standard argument in many libertarian circles. Penn Jillette made the same argument about the abortion pill on Glenn Beck's show "The Blaze." The pharmacist's conscience trumps yours, so just go to another pharmacist. Never mind if there are not any nearby. Never mind that it is your body. I blogged about that broadcast before in my post "Hobby Lobby Horse Hockey."
It was also the same reasoning behind Kim Davis' recent refusal to issue marriage licenses to LBGT couples. The only two differences are that: 1) Kim Davis is an actual individual rather than a corporation and 2) She is a government official and we have a little thing in this country called the separation of church and state. But the basic attitude is the same across these examples.
And if such "libertarians" like Paul, Beck, and Jillette think people in these gatekeeper professions should be allowed to discriminate, small wonder Paul thinks that any employer should be allowed to.
Obviously, this paleo-libertarian reasoning is a boon for bigots and bullies of all sorts because it lets them redefine private oppression as personal freedom. Don't want to sleep with the boss to keep your job or get that promotion? Go work someplace else. Accordingly, it has been embraced by conservatives parroting "libertarian" rhetoric. Conservatives are temperamentally authoritarian in their political outlook, but they like to pretend to be libertarians so this argument is rhetorical catnip for them.
But this is a familiar situation. Abraham Lincoln had once pointed out that the wolf and the sheep have very different definitions of liberty - which is why slave holders called him a "tyrant."
The world has never had a good definition of the word liberty, and the American people, just now, are much in want of one. We all declare for liberty; but in using the same word we do not all mean the same thing. With some the word liberty may mean for each man to do as he pleases with himself, and the product of his labor; while with others the same word may mean for some men to do as they please with other men, and the product of other men’s labor. Here are two, not only different, but incompatable things, called by the same name—liberty. And it follows that each of the things is, by the respective parties, called by two different and incompatable names—liberty and tyranny.
The shepherd drives the wolf from the sheep’s throat, for which the sheep thanks the shepherd as a liberator, while the wolf denounces him for the same act as the destroyer of liberty, especially as the sheep was a black one. Plainly the sheep and the wolf are not agreed upon a definition of the word liberty; and precisely the same difference prevails to-day among us human creatures, even in the North, and all professing to love liberty. Hence we behold the processes by which thousands are daily passing from under the yoke of bondage, hailed by some as the advance of liberty, and bewailed by others as the destruction of all liberty. Recently, as it seems, the people of Maryland have been doing something to define liberty; and thanks to them that, in what they have done, the wolf’s dictionary, has been repudiated.
It has been repeatedly repudiated, but it's still in print because there are always new editions.