Are there any [beliefs that fall within this penumbra] that make you cringe?
I am tempted to say that the question itself is an example of something that makes me cringe.
I often find it helpful to attempt to downplay the moral significance of tribal identity. As a first approximation, the morally significant unit is the individual, and the moral significance of each individual is equal. That is an admittedly vague statement, which could lead in a number of directions. For me, it connects to the doctrine of free trade and to the non-aggression principle. It connects to a view that there is no spiritual "we" that inhabits government institutions. It connects to a view that the democratic majority is not a righteous authority; rather, it is at best an imperfect check on concentrated power.
Somewhat paradoxically, discussions of libertarian philosophy often strike me as exercises in what I think of as tribalism. Tribalism is concerned with distinguishing the in-group from the out-group, excommunication of unwanted members, and establishing status within the tribe. So, for example, you might give a libertarian purity test.
I think that tribalism pervades our society. We are often hypocritical about it. The guy who informs you that circumcision or a head scarf is a primitive manifestation of tribal identity while he is wearing an earring. The guy who is proud of his racial tolerance while dismissing people over 40 as not not worth listening to. The guy who complains that Christians are dogmatic and intolerant while sneering at "global warming deniers."
Suppose that I express a belief, and you write a critical response. Consider two ways of framing the response.
1. Your belief has the following problems:
2. Your belief makes you a non-libertarian because:
I think that (2) smacks of tribalism. I would rather not care about whether expressing a particular belief makes me a libertarian. I would prefer to care about whether it is sound.
Bryan's question has both aspects to it. On the one hand, he is asking us about what beliefs we think are sound or unsound. On the other hand, there is a presumption that in this exercise we will search among the set of beliefs held by people who belong to a tribe called libertarians.