There's a big difference, though. LSU and McNeese don't compete on the same level, so LSU doesn't really care about McNeese in that regard. McNeese winning Division I-AA championships doesn't affect LSU in the same way that UL going 9-3 in football would.
I'm sure there were a ton of Youngstown State/Ohio State fans and Troy/Auburn fans at one point too. Right now, McNeese fans don't have to make a "choice" between the two. That would/will change if McNeese ever moves to Division I-A and starts competing in the same "division" as LSU. LSU fans won't be as forgiving toward McNeese and vice versa.
For the record, I have no problem with the "house divided" phenomena we have in Lafayette. My observation was that in traveling to other college towns, those cities seem to get behind the university a lot more than Lafayette "gets behind" UL.