I have a class that includes some auxiliary functions that do not operate on object data. Ordinarily I would leave these methods private, but I am in Python so there is no such thing. In testing, I am finding it slightly goofy to have to instantiate an instance of my class in order to be able to call these methods. Is there a solid theoretical reason to choose to keep these methods non-static or to make them static?
If a method does not need access to the current instance, you may want to make it either a classmethod, a staticmethod or a plain function.
A classmethod will get the current class as first param. This enable it to access the class attributes including other classmethods or staticmethods. This is the right choice if your method needs to call other classmethods or staticmethods.
A staticmethod only gets it's explicit argument - actually it nothing but a function that can be resolved on the class or instance. The main points of staticmethods are specialization - you can override a staticmethod in a child class and have a method (classmethod or instancemethod) of the base class call the overridden version of the staticmethod - and eventually ease of use - you don't need to import the function apart from the class (at this point it's bordering on lazyness but I've had a couple cases with dynamic imports etc where it happened to be handy).
A plain function is, well, just a plain function - no class-based dispatch, no inheritance, no fancy stuff. But if it's only a helper function used internally by a couple classes in the same module and not part of the classes nor module API, it's possibly just what you're looking for.
As a last note: you can have "some kind of" privacy in Python. Mostly, prefixing a name (whether an attribute / method / class or plain function) with a single leading underscore means "this is an implementation detail, it's NOT part of the API, you're not even supposed to know it exists, it might change or disappear without notice, so if you use it and your code breaks then it's your problem".
Should methods that do not act on object data be made static?