I'm a libertarian. Note the small l-- I'm not associated with the political party. I don't know whether I've never said anything to give you an impression of my politics, or if you haven't noticed.
L(l)ibertarianism is a good bit older than the Tea Party, and frequently more sophisticated, not that that's difficult. Also, as with any group of people of any size which has been around for a while, there isn't total internal agreement.
I recommend The Agitator
as a libertarian blog which is considerably better than your stereotype, and Unqualified Offerings
as a similar libertarianish blog-- I can't remember whether the folks there still identify as libertarians.
Actually, I don't just recommend the blogs-- I think you need to read them to expand your view of what's going on. The Agitator, in particular, specializes in justice system atrocities, and I don't know of any other blog (of any political persuasion) which is as good on the subject.
The reason liberals might have something to gain from association with carefully chosen libertarians (I grant that conservative-flavored libertarians are more common than liberal-flavored libertarians) is that you can use all the people who care about civil liberties that you can get. There isn't any mainstream pressure to care about civil liberties, and it doesn't speak well for the country.
Since I haven't been following the LP in general, I don't know whether the Texas LP is typical-- it sounds fringier than I would have expected.
Would you have been offended by the video if you weren't slotting in your pre-existing ideas about Libertarians?