I face exactly this problem with my navy 240.
The strap on one side is thick and firm..the other one is really thin, "furry" and full of creases. It also curls up on itself. Looks awful and that's why I don't carry it any more. The mounting loop for the strap on one side is so thin, it has stretched, whereas the other is normal.
I wrote to Filson and asked them as to what I should do..I got a "don't worry, this is normal and if you are unsatisfied, send it back",...