Is it possible to anchor a cabinet to a wall without damaging it?
This is a tall unit and if it were fully loaded, it could really hurt someone (especially a child) should it fall.  Products like the 3M command strips are designed for hooks where the force on them is acting downwards.  Your cabinet on the other hand, should it tip, would be pulling away from the wall and I really don't think those strips would hold.  If it were my house and my kids, I would not trust them and would opt for a bracket.

As for glueing it, in all liklihood, it would just pull the paper layer of your drywall off with it. Even if it held, it would likely damage your walls more than a couple of holes for a bracket when it comes time to remove it.

For a solution to this, what I often see come with tall bookcases is a short strap (webbbing) with a screw and washer on both sides.  One side screws into the back of the bookcase, and the other should be screwed into a drywall anchor - ideally a toggle bolt since they don't easily pull out.  The washer is important to prevent the screw from pulling through the webbing.  This particular one below uses velcro, but I'd personally screw it into the back of the bookcase.


(source: themanlyhousekeeper.com)  

Alternatively a L bracket will work, but they tend to look ugly and depending how much clearance you have, can be really tight to install and/or remove.