When a crit is dealt, and you have shields, are Crits removed first or last? This has been a major bone of contention in our game group over the past while.

So as an example, Luke has 2 shields and Whisper deals 2 hits and 2 Crits. Which make it through?

As per page 13 and 16 of the rulebook. Normal damage is suffered first, then critical damage. In your example Luke would suffer 2 critical damage.

Yes, normal damage is always dealt before critical damage. So in your example, if Luke didn't evade anything the two normal damage takes out his shields, then the two crits go to his hull.