Bear Country is a micronation
Notice how we never seem to hear about the other communities aside from Bear County, and why Officer Marguerite appears to be the only police officer we ever see. The possible one-man police force is probably also why Raffish Ralph is usually a Karma Houdini. The Bear family is running from the federal government
That's why they use assumed names - Mama, Papa, Sister, and Brother. There is no shoe store in Bear Country.
That can imply why all the bears are generally shoeless. A new Berenstain Bears TV Show would feature LGBTQ+
Maybe Brother and/or Sister Bear will meet another friend with two moms or two dads, or a cub who's transgender. Brother Bear knows more about dinosaurs than Sister Bear
Brother likes dinosaurs, but is it possible that Sister knows more about them than he does? In The Messy Room, they have an argument about cleaning their room.Sister: How am I supposed to sweep with your dumb dinosaur toys all over the floor?
Brother: They're not toys—they're models! And don't move them! I'm working on a set-up of the Pleistocene Age!
Sister: Pleistocene schmeistocene!
Sister's "Pleistocene schmeistocene" retort suggests that she knows more about dinosaurs than Brother does. Non-avian dinosaurs lived only during the Mesozoic era, going extinct long before the Pleistoscene.
Mama was pregnant with Brother when she and Papa were married.
According to the late Stan Berenstain, Papa is 29 years old and Mama is 27. Since Brother is 8 years old, this means Mama was just 19 when she gave birth to him. Despite the Retro Universe, they're still clearly living in the 20th century, so it's surprising that they would have gotten married before Mama was 21. Maybe they got a little too amorous while dating in their college-aged years, and had to get married early. Cousin Freddy is related to the Bear family on both sides - his mother is Mama's sister, his father is Papa's cousin.
In the books, Freddy's parents are Aunt Min and Uncle Wilbur. But Uncle Wilbur was first introduced as Cousin Wilbur in The Berenstain Bears and the Sitter. This isn't necessarily a Series Continuity Error: Wilbur could be both a cousin and an uncle-by-marriage. Great Natural Bear's lifestyle is by choice.
Great Natural Bear was created out-of-universe to show "natural" bear behaviors in contrast to the humanlike life of the "civilized" bears seen elsewhere in the books. In-universe, he stands out as the only bear in Bear Country who lives in a cave, hibernates, doesn't wear clothes, and eats raw fish straight out of streams. Great Natural can speak English just fine, and if he wrote the "Great Natural Bear's Lair" sign outside his cave, he can also write it, so he may be a "civilized bear" who simply chooses to live as The Hermit, perhaps for philosophical or religious reasons. The "Great Natural" in his name may indicate the rest of Bear Country respect him as a Hermit Guru (they certainly don't seem to have any problem with their cubs hanging around with a naked guy who lives in a cave, at least.)