It's sad, but theft happens far too often at WDW, and not just pickpockets and such. Cars get broken into in the parking lots. Valuables left out in hotel rooms disappear. You hear about incidents over and over.
We will always stay onsite, in part so that we can take advantage of the room charge feature. We take virtually no cash with us to WDW, and use the room charge as much as possible. The only cash we ever need is for the odd snack at a popcorn cart, and even more and more of those are taking the room charge now. Eventually, we're hoping that we can do Disney as an entirely cash-free vacation. No cash on your person or in your room, and all the credit cards locked in the room safe, means nothing to steal, after all.
My other tip (learned the hard way) is to assign one member of the party to lock the room safe before leaving the room, and a second one to double-check that they've done it.

If everyone assumes that someone else will do it, usually the result is that no one does. And, unfortunately, although the door lock supposedly tracks which keys have entered when, Disney Security can't (won't?) do anything about missing valuables from your room...just so's ya know...
I'm also a big fan of the fanny pack, although I'll wear it in front rather than behind. If all of my possessions are attached to me, and zipped up safely inside the bag, then they can't fall out on a ride or be forgotten at the restaurant. I put my room key and tickets in a separate zipped section of the bag that's easier to access, and not the same section that I have my ID in. The system works pretty well, and since I've started doing that the most I've lost is a pair of sunglasses.
While I go to Disney for the Magic, not everyone is there for the same reason unfortunately...