Personally, I can't think of anything more lukewarm than the people involved who say they're neutral.
Why does some society about promoting Gregory Chant, for example, need to have an official position on everything that all their members must hold? Individuals in their society may have their own personal opinions, or maybe just don't know(and there's nothing wrong with that, it's less dangerous than pretending you know all the answers). But it doesn't mean the society as a whole must have a platform and position on every possible issue surrounding the Crisis, so that they know not to associate or work with any other Catholics who might have different views.
As for your definition of a fence-sitter, while I know you got it from a dictionary, I feel the definition you gave isn't the best and doesn't grasp the full meaning of it. A fence-sitter isn't just someone who's neutral, it's someone who claims to be neutral because they're afraid of picking a side because of the repercussions of doing so, e.g criticism from the other side. It doesn't apply to someone who's actually neutral just because they don't know or it's not relevant to them, etc.