If you use “thick libertarian” and “thin libertarian” to refer to individuals, you’re misunderstanding the terms. All libertarians are thin libertarians, and all libertarians are thick libertarians. Thin libertarianism is just the thin core that all libertarians agree on in so far as they’re libertarians, thick libertarianism is the additional beliefs that we add onto those in order to have a more full understanding of libertarianism. The view that only the “thin” aspects matter is itself a “thick” view, since the “thin” aspects don’t directly entail that.
So, the right question to discuss is not “thin libertarianism vs. thick libertarianism” (especially since the two depend on each other), but 1. “is it possible to have libertarianism without thickness, and if so, does this mean thickness is not actually relevant to libertarianism-per-se?” and 2. “what is the correct thickness orientation?”
Also, another reason why thick libertarianism is conceptually necessary is that extra-NAP beliefs are necessary in order to apply non-aggression. Questions like animal rights and the details of children’s rights can’t be answered by literally only referencing the NAP by itself, so in order to determine whether or not a given action taken against a child or animal is a rights-violation, you have to have a thicker conception of libertarianism.