Concerns about hanging a hundred plus mugs on dry wall
It's hard to say whether your drywall will support this, it might, it might not.  Big factors are the thickness, condition, and stud spacing.  As well, if the bars ever experience a dynamic load like someone bumping into it, pulling on mugs, etc. it might very well fail while it was fine with a static load.

The "right" way to do this is to open up the walls and install blocking between studs so that you can mount your bars to a solid support instead of the drywall.  Or alternatively, install a piece of plywood on top of the drywall, anchored to the studs, and then mount your bars to the plywood. You could paint it to match the wall.