Theories

Together Theory
'And We're One Of Them' -Bert August 18th 2015

This theory suggests that Ernie and Bert are indeed one being. This is suggested because Ernie and Bert are always together in scenes. The theory was created by Victortoise.

Proof
In the 'Our New Show! Character Introduction' Bert says the line 'And We're one of Them' when referring the fact that they will be part of the new show.

Ernie and Bert RPG has both Ernie and Bert together in an adventure for the golden almond/peanut. They don't mention anything about them as one being, but nobody says it's false either.

Other Occurrences;

Stuffed News Episode 2

The Jerry Show Season 2 Episode 2

The Burglary

Stuffed Stereotypes Episode 1

Debunking
In Episode 2 of Stuffed Stereotypes, Bert is seen outside ALONE with Ernie nowhere to be seen. This could mean this theory is false or Ernie is off-camera.

Final Thoughts
While this theory sounds completely wrong, there is little to no proof this is fake. They very well could be one organism.

Stuffed Stereotypes Is a Concentration Camp?
'Go into Your Groups' Bert July 3rd 2016