We could argue about it but it is off topic and that would be disrespectful to the thread creator.
Rand Paul is a Republican not a Libertarian.
Maybe you are confusing him with his father?
Rand Paul is a libertarian republican, like his father.
Like his father, Rand has also officially been part of his movement’s official libertarian party.
Libertarians often like to operate from the GOP for two reasons, if they think they can use it to actually gain office, and also because they are fighting to move it left and make it more libertarian.