I don't think the Saints and LSU are Hatfields and McCoys. They are both Hatfields or McCoys, just from a slightly different branch of the family, but they are close. I think part of it for you is that you grew up a Tulane fan and that leads you to always see LSU as the enemy. The truth is that there is a huge cross-over between LSU and Saints fans. In fact, very few LSU fans aren't also Saints fans. The exception to that rule are the Baton Rouge natives that also went to LSU, but as far as LSU fans who aren't from Baton Rouge, almost all of them are also Saints fans.
And, I went to LSU too so I know the attitude toward New Orleans and people from there that you are talking about. But, I think you have confused the attitude of Baton Rouge natives as being the same as the attitude of LSU fans.