I was stuck in the middle of one of these at a megacorp. It was a Code Mauve, which meant it was technically enough to pre-empt my existing project. I grabbed a meeting with my manager, and carefully asked if I should find a way to avoid being pulled off my project. My manager just said to shelve my current project and work on the Code Mauve, as the rules designate.

When my manager got heat for the shelved project, he threw me under the bus and got me onto a PIP for not being able to complete tasks.