What's this grey bar doing in my war assets?

Solution 1:

The gray bar represents the total value your War Assets would be worth, if you had 100% Readiness Rating.

Without playing any of the multiplayer mode or the other tie-in games, your Readiness Rating will always be 50%. The more multiplayer you play, the higher the Readiness Rating, and the less gray bar (and therefore the more blue bar) you'll have.

Being at 50% means that you'll have to find 2x the amount of War Assets to get the same ending as a person who has 100%.

This mechanic is also explained in this question:

What is the difference between "Total Military Strength" and "Effective Military Strength"?

Solution 2:

They greyed out part of the bar shows how much military effectivness you lose due your galactic readiness. Since you have 50% readiness, 50% of your bar is grey, the full bar shows where you'd be with max readiness.