I made this and it tastes very vinegary. Is that normal? Is there something I can add to take the edge off?

Think of the finished shrub as a concentrate -- add liquid and sweetener to your taste. To me, about 2 tablespoons of the shrub with some still, some sparkling water and a few ice cubes in a 12 ounce glass is right for the ones that I've made. I like the tart taste!
The cider vinegar was used in traditional farmers' drinks in the summer months, for the electrolytes, when working hard out in strong hot sun. Switchel is another name for a traditional fruit/vinegar (usually) drink -- http://en.wikipedia.org/wiki/Switchel.

Yeah, shrubs are supposed to be pretty vinegary, since they pretty much are vinegar, but if it's too acidic for you, you could add extra sugar/honey/maple syrup to taste, and also drink it more diluted. I often put just a couple dashes of shrub in a large glass of sparkling water.

Thought I've never made this recipe; it is a shrub which is basically a drinkable vinegar. Perhaps the apples you used weren't sweet enough to balance with the cider vinegar. Try it again with a different kind of apple