Obstacles apply to monsters. Nothing in the rules says they don't. It is specified on page 19 that heroes act as obstacles to monsters, which means obstacles must also act as obstacles.
The traitor rules specifically state that the traitor can ignore obstacle tokens. Monster rules do not.
Monsters ignore white text on tiles.
This is not correct. They may not use actions on tiles, but they may use special movement rules on tiles just as the heroes and traitor may. And nothing says monsters don't suffer the effects of obstacles or fog on a tile.