dir is a convenience function that most of the time delegates to the object’s __dir__ implementation (only performs an inspection if cannot find it).
There are several __dir__ implementations in Python’s code (modules, classes, other objects, …) and each one displays the most relevant information for an interactive context with different criteria, as do so many other __dir__ implementations in the vast Python ecosystem. Presuming the normality of an attribute on the basis of underscores sounds kinda dunderphobic to me 
Sorry, just kidding. What I mean is that since dunders are only a convention (except in the case of name mangling), often it would be difficult to know what kind of information is being hidden.
IMO this is a case that fits perfectly with the purpose of PYTHONSTARTUP. I usually have a very small wrapper over dir() in mine to identify methods at a glance and I found it very convenient. Adapted to your idea, would be something like this:
def ddir(obj):
return [a + '()' if callable(getattr(obj, a)) else a
for a in dir(obj) if not (a[:2] == '__' == a[-2:])]