No, you can't scratch glass with soft plastic. If you're dealing with something really early - like pontil-era - then it couldn't hurt to be better safe than sorry, but I have used far harsher things on more recent bottles without causing any scratches.
I use the stiffest bristle toothbrush made. Works great. As CanadianBottles says plastic will not scratch glass, it is softer than glass. You can also use brass bristle brushes as brass is softer than glass. It must be brass though. Steel of any kind, bbs, steel pads, brushes etc. will scratch glass as glass is softer than steel.
The only way that I can see scratches resulting from using a toothbrush would be from sand being carried in the bristles, and even that would be pretty unlikely unless you're not using any water and soap. And as mentioned above, the scratches would not be from the plastic bristles themselves.