“Does Libertarianism dominate the Party?”
In short, “No.”
The consensus that seemed to emerge from the name debate was that we congregate around a set of beliefs that could be characterised as libertarian-left.
The quotes you have cited without context all related to problems with the public perception of “libertarian” as the right wing “every man for himself” flavor of libertarian. Essentially, all the labels in politics are broken, so even using the word “libertarian” with a modifier doesn’t help with public perception, and maybe even with your own.
Libertarian-left is different. It means we care about social issues, and in fact take them as our primary motivation, but seek to resolve them in ways that are minimally authoritarian.