How much of a disadvantage is the restriction on purple items in F2P?

Not much of a disadvantage at all, you can easily complete all of the single player and story content with only greens and blues (but it would be easier with a friend or two). Granted, you might have to grind a little more for levels (instead of grinding for purples, so what difference does it really make). Purple items are not much of a benefit to hunt down at low levels anyway since you will out-level their usefulness quickly.

At higher levels, they are extremely important for pvp, because they will give you the necessary edge to win fights. They are also pretty important for end-game raids, because you'll need them to survive and get... the other purple items.

But for the main story, as much as they might help they are not a necessity.