Has anyone ever played a game where "The Butcher" and "Ogden's Sign" were both active?

The strategy guide and the gamepedia wiki both say that those two quests, and "Gharbad the Weak", are part of a set of mutually exclusive quests, and two out of three of them will be available on any given playthrough. So the odds should come down to this:

"The Butcher" and "Gharbad the Weak": 1/3
"The Butcher" and "Ogden's Sign": 1/3
"Gharbad the Weak" and "Ogden's Sign": 1/3

You're correct that those three quests are in a group, and that you'll randomly get two out of the three in any game. But I haven't seen anything confirming that each quest has an equal chance of being chosen. Certain quests may have a higher chance of appearing, or two quests may have a higher chance of being selected together. I haven't seen anything to confirm that theory either, but I'm just saying it may not be a simple 1/3 chance for each.

To your specific question: yes, I've seen both The Butcher and Ogden's Sign appear in the same game. I don't have a large enough data set (nor have I been actually tracking it) to say that it has happened in 33% of my games. But yes, it is possible.

The way it picks the quests (for single-player) is it first enables everything, then picks one quest (randomly) in each group to disable.