One thing not noted so far in answers is the motion of the sun during the seasons.

It's made clear through several books that summer happens when the sun rises and sets near the rim-hub line. Winter happens when it rises/sets perpendicular to that line.

This means that one summer the sun moves across the sky in one direction, and the next summer (summer II or summer segundus) it move the opposite direction! It takes 800 discworld days for the sunrise to return to the same location.

This means it's pretty obvious to everyone the world is a disc.

But, as to how widespread is knowledge of whether the disc is on the back of 4 elephants standing on a giant turtle, that is a much harder answer.

Depending on which time period and which part of the disc you want your answer to come from, we get - very limited to fairly well spread.

The Omnian view is odd because of their stance on globe versus disc, not because of space turtle. The knowledge of the space turtle seems to be limited to people like Didactylos or the Omnian captain who have had the opportunity to see over the Rim.

But Small Gods is set many hundreds of years before most Discworld novels. By the time of Rincewind, we see evidence that the knowledge of the existence of the turtle is more widespread. But, again, this knowledge can still be limited - particularly in more "traditional" parts, like Lancre (home of Granny Weatherwax). It's like people here knowing the earth is round and moves around the sun, but not understanding space-time curvature.

One thing not noted so far in answers is the motion of the sun during the seasons.

It's made clear through several books that summer happens when the sun rises and sets near the rim-hub line. Winter happens when it rises/sets perpendicular to that line.

This means that one summer the sun moves across the sky in one direction, and the next summer (summer II or summer segundus) it move the opposite direction! It takes 800 discworld days for the sunrise to return to the same location. But there's only 400 days between midwinters.

This means it's pretty obvious to everyone the world is a disc.

But, as to how widespread is knowledge of whether the disc is on the back of 4 elephants standing on a giant turtle, that is a much harder answer.

Depending on which time period and which part of the disc you want your answer to come from, we get - very limited to fairly well spread.

The Omnian view is odd because of their stance on globe versus disc, not because of space turtle. The knowledge of the space turtle seems to be limited to people like Didactylos or the Omnian captain who have had the opportunity to see over the Rim.

But Small Gods is set many hundreds of years before most Discworld novels. By the time of Rincewind, we see evidence that the knowledge of the existence of the turtle is more widespread. But, again, this knowledge can still be limited - particularly in more "traditional" parts, like Lancre (home of Granny Weatherwax). It's like people here knowing the earth is round and moves around the sun, but not understanding space-time curvature.