There are myriad posts on vegetarian friendly places on this forum if you do a search, this subject comes up quite often.
If you eat seafood (and even if you don't) you shouldn't have a problem anywhere you go in the city or suburbs and you won't be limiting yourself, you'll be able to experience classic New Orleans cuisine and establishments.
I vacillate between vegetarian and pescetarian and never have a problem and I live in N.O.
ps Pork does not flavor everything nor are alligators transportation (just kidding)
2 Links to recent posts re this topic:
2 examples of many!!!!!!! seafood options:
Mandina's in Mid City on Canal St:
Bon Ton ...dowtown N.O.
3800 Canal St, New Orleans, LA 70119
Bon Ton Cafe
401 Magazine St, New Orleans, LA 70130