Saints never shared a division with Seattle. That's why they "respect" Seattle.
There's layover beef with SF from the Dome Patrol days when they were the opposite team that they are now. I'm sure if the Seahawks ever had to play a real meaningful game against an AFC West team, the hate would return.
They're a pretty fortunate franchise that had a lot go right for them after 2005. Nabbed Brees and Payton, and nearly missed the super bowl in 2009 -- Vikings could have very easily won that game. And then there's bounty gate as well.
You guys knocked them out of the playoffs in what probably annoys teams league wide with the playoff format of division winner hosting wildcard teams regardless of records.
We will see how much longer the Seahawks/Saints love fest lasts. My guess is it comes to an end this year.