Is Chabad ultra-Orthodox?

Despite (or perhaps because of) my distaste for labelling Jews, I was recently involved in an online debate as to whether Chabad is "ultra-Orthodox" (where I argued that it is not). This led to some self-reflection and research.

Humankind have been been involved in the process of taxonomy since the dawn of time. Hashem brought all the animal kingdom before Adam Harishon and he identified them by their "names", thus grouping and categorizing them.