Yes, Disney World allows guests to carry their park bags onto the rides and attractions. I typically just hold my bag on my lap or set it beside me on the rides.  The only rides you may want to reconsider bringing your bag on include Kali River Rapids at Animal Kingdom and Splash Mountain at Magic Kingdom. Since these are water rides, you’ll want to make sure your electronic items are secure in a Ziplock or waterproof bag. If you don't want to carry your bag onto the rides, you can leave them in your stroller in the designated parking areas. I recommend removing any valuables just in case, but we’ve never had a problem finding our stroller and bag after exiting an attraction. Walt Disney World also offers lockers for rent if you prefer to use them. However, we don’t find them to be very convenient for park touring.