Sorry you had items stolen, OP. Even if they were items you could afford to lose, that doesn't mean you wanted to lose them. I agree with the pp in that I have seen people leave things on strollers like purses and cameras, and I wonder "What are they thinking?". Just like the pizza flyer scammers that troll the resorts, I'm sure there are theme park thieves looking to make a quick buck by taking your stuff. I don't even carry a bag with me these days - everything goes in pockets. But I do the same thing if I go to the grocery store or mall - it's not just a WDW thing.
As far as illness goes, I haven't gotten ill at Disney since I started carrying the individually wrapped Wet Ones towellettes and using one before I eat ANYTHING at the parks or resorts. Even if you stop in the rest room to wash before going to the restaurant, you will touch things other people have touched (when was the last time that paper menu was cleaned, hmmmm?). I don't touch any silverware or anything until I'm ready to eat and once I have my food ready, I wash and I eat. I also never touch my face when out in public, because it's easy to catch an illness that way. I also try to allow a few feet between myself and the person in front of me in line whenever possible, so I have some room to move if the person behind me starts sneezing and coughing. Other than that, I don't worry about what I touch, or who might have touched it before me.
I don't feel I'm any more likely to get sick at WDW than anywhere else. In fact, I feel I'm less likely to get sick at WDW than I am at work, because at work we all work very closely in one room with a secured door that stays closed - so if someone comes in to work sick, it's really hard not to catch it (and a lot of them come in hoping they will be sent home so they don't have to bring a doctor note for the time off). A couple weeks before my January trip, there was just me and one other person in the office - everyone else was out sick! I use way more hand sanitizer and Lysol at work than I would ever use at WDW.