Well, I'm a little all over the place with this.
For Carboys, I do not rinse.Tools, glasses, etc. I wipe down after sanitize with a terry towel that is soaked with sulfite solution.Bottles, I do not rinse but I let them dry for a bit on the tree.
Then again, I usually know my Free SO2 So if the wine is on the high side I tend to rinse/dry more then if I know the SO2 is low.
I guess mostly I don't rinse but I wipe off.