I honestly don't see any problem if they have bands of pirates playing on one side of NOS and the songs from Frog Princess coming from a jazz quartet on the other side of the land.
Why would they have created Bear Country if guests weren't leaving Frontierland while they were in NOS. It's because once they left Frontierland, they were in Frontierland again. To not be confusing, that area became Frontierland II. AKA Bear Country. AKA Critter Country.
If this were not the case, and NOS was firmly set in the 1800s, the whole area would be called Frontierland, with New Orleans, Critter and Thunder Mesa areas. But that's not how it's ever really been. The two extra lands over there evolved out of Frontierland, but if you think they are still part of Frontierland, you're thinking of Yesterland and not the Disneyland that's there now.