As far as I know, you're seriously gimped if you go neutral... Another bad decision by Bioware.
No. There is no specifically "neutral" gear, but the light and dark side restricted gear is mostly appearances only. It is equivalent to crafted, dropped, and bought gear.
This means you will occasionally miss out on a drop (moreso than the light and dark side players, who will miss out on half as many), but the pieces so restricted are few and far between.
You are not "gimped" by any stretch of the imagination.