First, I address this later in my post. Using "== None" is a bad habit, there is simply no good reason to do it and lots of reasons not to, so students just shouldn't get in the habit of doing it in the first place.
Second, in the post I was responding to Nick was explicitly suggesting "== None” be treated as an equally-acceptable approach in general.
Others in this thread have looked into this and there are a wide variety of other types that will suffer.
More generally anything that raises an exception when given an invalid equality test, an extremely common idiom, will be fundamentally broken by this. It will be impossible to use them as arguments at all where "== None" is used, even in cases where they would otherwise work perfectly fine. Trying to do so will raise an exception.