You might find threads discussing relationship anarchy of interest. Search for threads tagged with 'anarchy', 'relationship anarchy' and 'RA'. Libertarianism and anarchism are not the same at all but in the context of relationships might be odd bedfellows.
And, at least in the US (and I realize your characters are not from the United States), libertarian has a very particular political bent, followers of Ayn Rand and such. I am quite libertarian in my views on sexuality and laws regarding sexuality (I believe that little is off the table for consenting adults and that laws about sexuality should be few and focused) but would not consider myself a libertarian at all. You may need to broaden your descriptive focus - but this is based solely on the unfortunately rather nutjob libertarian movement here in the US.